From af114330c7eedd55ff4c7bd5ea6cb51897426a1c Mon Sep 17 00:00:00 2001 From: Landon D. C. Elkind Date: Tue, 8 Dec 2020 12:47:07 -0700 Subject: principia TeX package updates and PDFs --- List of Definitions.pdf | Bin 0 -> 186185 bytes List of Definitions.tex | 446 ++++++++++++++++++++++++++++++++++++++++++++++++ principia.sty | 30 +++- 3 files changed, 470 insertions(+), 6 deletions(-) create mode 100644 List of Definitions.pdf create mode 100644 List of Definitions.tex diff --git a/List of Definitions.pdf b/List of Definitions.pdf new file mode 100644 index 0000000..734e405 Binary files /dev/null and b/List of Definitions.pdf differ diff --git a/List of Definitions.tex b/List of Definitions.tex new file mode 100644 index 0000000..0dc4c06 --- /dev/null +++ b/List of Definitions.tex @@ -0,0 +1,446 @@ +\documentclass[12pt,openany,leqno,twocolumn]{book} +%Principia package requirements +\usepackage{pifont} %This loads the eight-pointed asterisk. +\usepackage{marvosym} %This loads the male and female symbol. +\usepackage{graphicx} %This loads commands that flip iota for definite descriptions, Lambda for the universal class, and so on. The (superseded) graphics package should also work here, but is not recommended. +\usepackage{amssymb} +\usepackage{amsmath} +\usepackage{fullpage} +\usepackage{perpage} +\usepackage[T1]{fontenc} +\usepackage[utf8]{inputenc} +\usepackage{mathrsfs} +\usepackage[hidelinks,pdfencoding=unicode]{hyperref} +\usepackage{enumitem} +\usepackage{moreenum} +\usepackage[normalem]{ulem} +\usepackage[perpage,symbol]{footmisc} +\usepackage{setspace} + +%Meta-logical symbols +\newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof. +\newcommand{\pmsub}[2]{\bigg \lbrack \small \begin{array}{c} #1 \\ \hline #2 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmsubb}[4]{\bigg \lbrack \small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmsubbb}[6]{\bigg \lbrack \small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmsubbbb}[8]{\bigg \lbrack \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmthm}{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}} %This is the theorem sign. +\newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number. +\newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol\cdot$}}} %This is a sign introducing a theorem sub-number. +\newcommand{\pmdf}{=_\text{Df}} +\newcommand{\pmpp}{\text{Pp}} + +%Square dots for scope, defined for up to six dots +\newcommand{\pmdot}{\mathop{\hbox{\rule{.3ex}{.3ex}}}} +\newcommand{\pmdott}{\mathop{\overset{\pmdot}{\pmdot}}} +\newcommand{\pmdottt}{\pmdott \pmdot} +\newcommand{\pmdotttt}{\pmdott\pmdott} +\newcommand{\pmdottttt}{\pmdott\pmdott\pmdot} +\newcommand{\pmdotttttt}{\pmdott\pmdott\pmdott} + +%Logical connectives +\newcommand{\pmnot}{\mathord{\sim}} +\newcommand{\pmimp}{\boldsymbol{\supset}} +\newcommand{\pmiff}{\equiv} +\newcommand{\pmor}{\boldsymbol{\vee}} +\newcommand{\pmall}[1]{(#1)} +\newcommand{\pmsome}[1]{(\text{\raisebox{.5em}{\rotatebox{180}{E}}}#1)} +\newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{E}}}} +\newcommand{\pmand}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}} +\newcommand{\pmandd}{\overset{\pmand}{\pmand}} +\newcommand{\pmanddd}{\pmandd\hspace{.1em}\pmand} +\newcommand{\pmandddd}{\pmandd\hspace{.1em}\pmandd} +\newcommand{\pmanddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmand} +\newcommand{\pmandddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmandd} + +%Additional defined logic signs +\newcommand{\pmhat}[1]{\mathbf{\hat{\text{$#1$}}}} +\newcommand{\pmpf}[2]{#1#2} %for propositional functions of one variable +\newcommand{\pmpff}[3]{#1(#2, #3)} %for propositional functions of two variables +\newcommand{\pmpfff}[4]{#1(#2, #3, #4)} %for propositional functions of three variables +\newcommand{\pmshr}{\textbf{!}} %*12.1 and *12.11, used for predicative propositional functions +\newcommand{\pmpred}[2]{#1\pmshr#2} %for predicates (``predicative functions'') of one variable +\newcommand{\pmpredd}[3]{#1\pmshr(#2, #3)} %for predicates (``predicative functions'') of two variables +\newcommand{\pmpreddd}[4]{#1\pmshr(#2, #3, #4)} %for predicates (``predicative functions'') of three variables +\newcommand{\pmnid}{\mathrel{\ooalign{$=$\cr\hidewidth\footnotesize\rotatebox[origin=c]{210}{\textbf{/}}\hidewidth\cr}}} %*13.01 +\newcommand{\pmiota}{\rotatebox[origin=c]{180}{$\iota$}} %the rotated Greek iota used in definite descriptions +\newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01 +\newcommand{\pmDsc}{\pmiota} %*14.01 +\newcommand{\pmexists}{\text{E}\pmshr} %*14.02 + +%Class signs +\newcommand{\pmcuni}{\text{\rotatebox[origin=c]{180}{$\Lambda$}}} +\newcommand{\pmcnull}{\Lambda} +\newcommand{\pmcls}[2]{\pmhat{#1}(#2)} +\newcommand{\pmCls}{\text{Cls}} +\newcommand{\pmClsn}[1]{\text{Cls}^{#1}} +\newcommand{\pmcexists}{\text{\raisebox{.5em}{\rotatebox{180}{E}}}\mathop{\pmshr}} +\newcommand{\pmccmp}[1]{\boldsymbol{-}#1} +\newcommand{\pmcmin}[2]{#1\boldsymbol{-}#2} +\newcommand{\pmcin}{\mathop{\epsilon}} +\newcommand{\pmccup}{\mathop{\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}}} +\newcommand{\pmccap}{\mathop{\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}}} +\newcommand{\pmcinc}{\mathop{\boldsymbol{\subset}}} + +%Relation signs +\newcommand{\pmruni}{\dot{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}} +\newcommand{\pmrnull}{\dot{\Lambda}} +\newcommand{\pmdscf}[2]{#1\textbf{`}#2} +\newcommand{\pmdscff}[2]{#1\textbf{`}\textbf{`}#2} +\newcommand{\pmdscfff}[2]{#1\textbf{`}\textbf{`}\textbf{`}#2} +\newcommand{\pmdscfr}[2]{#1_{\pmcin}\textbf{`}#2} +\newcommand{\pmdscfR}[1]{#1_{\pmcin}} +\newcommand{\pmdscfe}[2]{\mathop{\text{E}}\mathop{\pmshr\pmshr}\pmdscff{#1}{#2}} +\newcommand{\pmdm}[1]{\text{D}\textbf{`}#1} +\newcommand{\pmDm}{\text{D}} +\newcommand{\pmcdm}[1]{\text{\rotatebox[origin=c]{180}{D}}\textbf{`}#1} +\newcommand{\pmCdm}{\text{\rotatebox[origin=c]{180}{D}}} +\newcommand{\pmcmp}[1]{C\textbf{`}#1} +\newcommand{\pmCmp}{C} +\newcommand{\pmfld}[1]{F\textbf{`}#1} +\newcommand{\pmFld}{F} +\newcommand{\pmrel}[3]{\pmhat{#1}\pmhat{#2}#3} +\newcommand{\pmrele}[5]{#1\{\pmhat{#2}\pmhat{#3}#4(#2, #3)\}#5} +\newcommand{\pmrelep}[3]{#1\{#2\}#3} +\newcommand{\pmrcmp}[1]{\ooalign{$\hidewidth\raisebox{.25em}{$\cdot$}\hidewidth$\cr$\mathbf{\pmccmp}$}#1} +\newcommand{\pmrmin}[2]{#1\mathrel{\ooalign{$\hidewidth\raisebox{.25em}{$\cdot$}\hidewidth$\cr$\mathbf{\pmccmp}$}}#2} +\newcommand{\pmrexists}{\dot{\mathop{\text{\raisebox{.5em}{\rotatebox{180}{E}}}}}\mathop{\pmshr}} +\newcommand{\pmcrel}[1]{\breve{#1}} +\newcommand{\pmCnv}{\text{Cnv}} +\newcommand{\pmcnv}[1]{\breve{#1}} +\newcommand{\pmcnvr}[1]{\text{Cnv}\textbf{`}#1} +\newcommand{\pmrcup}{\mathrel{\ooalign{$\hidewidth\cdot\hidewidth$\cr$\mathbf{\pmccup}$}}} +\newcommand{\pmrcap}{\mathrel{\ooalign{$\hidewidth\raisebox{.3em}{$\cdot$}\hidewidth$\cr$\mathbf{\pmccap}$}}} +\newcommand{\pmrinc}{\mathrel{\ooalign{$\hidewidth\cdot\hidewidth$\cr$\mathbf{\pmcinc}$}}} +\newcommand{\pmrrf}[2]{\overset{\boldsymbol{\rightarrow}}{#1\textbf{`}}#2} +\newcommand{\pmRrf}[1]{\overset{\boldsymbol{\rightarrow}}{#1}} +\newcommand{\pmrrl}[2]{\overset{\boldsymbol{\leftarrow}}{#1\textbf{`}}#2} +\newcommand{\pmRrl}[1]{\overset{\boldsymbol{\leftarrow}}{#1}} +\newcommand{\pmsg}[1]{\text{sg}\textbf{`}#1} +\newcommand{\pmgs}[1]{\text{gs}\textbf{`}#1} +\newcommand{\pmSg}{\text{sg}} +\newcommand{\pmGs}{\text{gs}} +\newcommand{\pmRprd}{\mathop{|}} +\newcommand{\pmrprd}[2]{{#1}\mathop{|}{#2}} +\newcommand{\pmrprdn}[2]{#1^{#2}} +\newcommand{\pmrld}[2]{#1 \boldsymbol{\upharpoonleft} #2} +\newcommand{\pmrlcd}[2]{#1 \boldsymbol{\upharpoonright} #2} +\newcommand{\pmrlf}[3]{#1 \boldsymbol{\upharpoonleft} #2 \boldsymbol{\upharpoonright} #3} +\newcommand{\pmrl}[2]{#1 \boldsymbol{\uparrow} #2} +\newcommand{\pmrlF}[2]{#1 \mathbin{\ooalign{$\upharpoonright$\cr\hidewidth\rotatebox[origin=c]{180}{\text{$\upharpoonleft$}}\hidewidth\cr}} #2} +\newcommand{\pmop}{\mathop{\text{\Female}}} +\newcommand{\pmopc}[2]{#1 \mathop{\underset{\textbf{''}}{\text{\Female}}} #2} + +%Products and sums of classes of classes or relations +\newcommand{\pmccsum}[1]{p\textbf{`}#1} +\newcommand{\pmccprd}[1]{s\textbf{`}#1} +\newcommand{\pmcrsum}[1]{\dot{p}\textbf{`}#1} +\newcommand{\pmcrprd}[1]{\dot{s}\textbf{`}#1} +\newcommand{\pmRprdd}{\mathop{||}} +\newcommand{\pmrprdd}[2]{{#1}\mathop{||}{#2}} + +%Identity and Diversity +\newcommand{\pmrid}{I} +\newcommand{\pmrdiv}{J} +\newcommand{\pmcunit}[1]{\iota\textbf{`}#1} +\newcommand{\pmcUnit}{\iota} +\newcommand{\pmcunits}[1]{\breve{\iota}\textbf{`}#1} + +%Cardinal numbers +\newcommand{\pmcn}[1]{#1} + +%Ordinal numbers +\newcommand{\pmrn}[1]{#1_r} +\newcommand{\pmdn}[1]{\dot{#1}} +\newcommand{\pmoc}[2]{#1 \boldsymbol{\downarrow} #2} + +%Subclasses and subrelations +\newcommand{\pmscl}[1]{\text{Cl}\textbf{`}#1} +\newcommand{\pmsCl}{\text{Cl}} +\newcommand{\pmscle}[1]{\text{Cl ex}\textbf{`}#1} +\newcommand{\pmsCle}{\text{Cl ex}} +\newcommand{\pmscls}[1]{\text{Cls}\textbf{`}#1} +\newcommand{\pmsrl}[1]{\text{Rl}\textbf{`}#1} +\newcommand{\pmsRl}{\text{Rl}} +\newcommand{\pmsrle}[1]{\text{Rl ex}\textbf{`}#1} +\newcommand{\pmsRle}{\text{Rl ex}} +\newcommand{\pmsrel}[1]{\text{Rel}\textbf{`}#1} +\newcommand{\pmRel}{\text{Rel}} +\newcommand{\pmReln}[1]{\text{Rel}^{#1}} +\newcommand{\pmrin}{\mathop{\epsilon}} + +%Relative type symbols +\newcommand{\pmrt}[1]{t\textbf{`}#1} +\newcommand{\pmrti}[2]{t^{#1}\textbf{`}#2} +\newcommand{\pmrtc}[2]{t_{#1}\textbf{`}#2} +\newcommand{\pmrtri}[2]{t^{#1}\textbf{`}#2} +\newcommand{\pmrtrc}[2]{t_{#1}\textbf{`}#2} +\newcommand{\pmrtrci}[3]{t_{#1}^{\text{ }#2}\textbf{`}#3} +\newcommand{\pmrtric}[3]{^{#1}t_{#2}\textbf{`}#3} +\newcommand{\pmrtdi}[2]{#1_{#2}} +\newcommand{\pmrtdc}[2]{#1(#2)} +\newcommand{\pmrtdri}[2]{#1_{#2}} +\newcommand{\pmrtdrc}[2]{#1(#2)} + +%Similarity relation signs +\newcommand{\pmrdc}[2]{#1\boldsymbol{\to}#2} +\newcommand{\pmsm}{\mathrel{\text{sm}}} +\newcommand{\pmsmbar}{\mathrel{\overline{\text{sm}}}} +\newcommand{\pmsmarr}{\overrightarrow{{\pmsm}}} +\newcommand{\pmonemany}{1\boldsymbol{\to}\pmCls} +\newcommand{\pmmanyone}{\pmCls\boldsymbol{\to}1} +\newcommand{\pmoneone}{1\boldsymbol{\to}1} + +%Selections +\newcommand{\pmselp}[1]{P_{\small\Delta}\mathbf{`}#1} +\newcommand{\pmSelp}{P_{\Delta}} +\newcommand{\pmsele}[1]{\pmcin_{\small\Delta}\mathbf{`}#1} +\newcommand{\pmSele}{\pmcin_{\Delta}} +\newcommand{\pmself}[1]{F_{\small\Delta}\mathbf{`}#1} +\newcommand{\pmSelf}{F_{\Delta}} +\newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}} +\newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1} +\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}}^2 \mathop{\text{excl}}} +\newcommand{\pmselc}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\boldsymbol{\mapsto}$}} #2} +\newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}} +\newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}} +\newcommand{\pmmultax}{\mathop{\text{Mult}} \mathop{\text{ax}}} + +%Inductive relations +\newcommand{\pmanc}[1]{#1_\pmast} +\newcommand{\pmancc}[1]{\pmcnv{#1}_\pmast} +\newcommand{\pmrst}[1]{#1_\text{st}} +\newcommand{\pmrts}[1]{#1_\text{ts}} +\newcommand{\pmpot}[1]{\text{Pot}\mathbf{`}#1} +\newcommand{\pmpotid}[1]{\text{Potid}\mathbf{`}#1} +\newcommand{\pmpo}[1]{#1_\text{po}} +\newcommand{\pmB}{B} +\newcommand{\pmmin}[1]{\text{min}_{#1}} +\newcommand{\pmmax}[1]{\text{max}_{#1}} +\newcommand{\pmMin}{\text{min}} +\newcommand{\pmMax}{\text{max}} +\newcommand{\pmgen}[1]{\text{gen}\mathbf{`}#1} +\newcommand{\pmGen}{\text{gen}} +\newcommand{\pmefr}[2]{#1\pmast#2} +\newcommand{\pmipr}[2]{I_{#1}\textbf{`}#2} +\newcommand{\pmjpr}[2]{J_{#1}\textbf{`}#2} +\newcommand{\pmfr}[2]{\overset{\boldsymbol{\leftrightarrow}}{#1}\textbf{`}#2} + +%Cardinality +\newcommand{\pmnc}[1]{\text{Nc}\textbf{`}#1} +\newcommand{\pmNc}{\text{Nc}} +\newcommand{\pmNC}{\text{NC}} +\newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1} +\newcommand{\pmNoc}{\text{N}_0\text{c}} + +\begin{document} + +\chapter*{\centering LIST OF DEFINITIONS} +\onehalfspacing +\begin{tabular}{l l} + \text{ }$\pmast1\pmcdot01$. & $p \pmimp q$ \\ + \text{ }$\pmast2\pmcdot33$. & $p \pmor q \pmor r$ \\ + \text{ }$\pmast3\pmcdot01$. & $p \pmand q$ \\ + \text{ }$\pmast3\pmcdot02$. & $p \pmimp q \pmimp r$ \\ + \text{ }$\pmast4\pmcdot01$. & $p \pmiff q$ \\ + \text{ }$\pmast4\pmcdot02$. & $p \pmiff q \pmiff r$ \\ + \text{ }$\pmast4\pmcdot34$. & $p \pmand q \pmand r$ \\ + \text{ }$\pmast9\pmcdot01$. & $\pmnot\{(\pmall{x})\pmdot \phi x\}$ \\ + \text{ }$\pmast9\pmcdot011$. & $\pmnot(\pmall{x})\pmdot \phi x$ \\ + \text{ }$\pmast9\pmcdot02$. & $\pmnot\{(\pmsome{x})\pmdot \phi x\}$ \\ + \text{ }$\pmast9\pmcdot021$. & $\pmnot(\pmsome{x})\pmdot \phi x$ \\ + \text{ }$\pmast9\pmcdot03$. & $(\pmall{x})\pmdot \phi x \pmdot \pmor \pmdot p$ \\ + \text{ }$\pmast9\pmcdot04$. & $p \pmdot \pmor \pmdot (\pmall{x})\pmdot \phi x$ \\ + \text{ }$\pmast9\pmcdot05$. & $(\pmsome{x})\pmdot \phi x \pmdot \pmor \pmdot p$ \\ + \text{ }$\pmast9\pmcdot06$. & $p \pmdot \pmor \pmdot (\pmsome{x})\pmdot \phi x$ \\ + \text{ }$\pmast9\pmcdot07$. & $(\pmall{x})\pmdot \phi x \pmdot \pmor \pmdot (\pmsome{x})\pmdot \phi x$ \\ + \text{ }$\pmast9\pmcdot08$. & $(\pmsome{x})\pmdot \phi x \pmdot \pmor \pmdot (\pmall{x})\pmdot \phi x$ \\ + $\pmast10\pmcdot01$. & $(\pmsome{x})\pmdot \phi x$ \\ + $\pmast10\pmcdot02$. & $\phi x \pmimp_x \psi x$ \\ + $\pmast10\pmcdot03$. & $\phi x \pmiff_x \psi x$ \\ + $\pmast11\pmcdot01$. & $(\pmall{x,y})\pmdot \phi(x, y)$ \\ + $\pmast11\pmcdot02$. & $(\pmall{x,y,z})\pmdot \phi(x, y, z)$ \\ + $\pmast11\pmcdot03$. & $(\pmsome{x,y})\pmdot \phi(x, y)$ \\ + $\pmast11\pmcdot04$. & $(\pmsome{x,y,z})\pmdot \phi(x, y, z)$ \\ + $\pmast11\pmcdot05$. & $\phi(x, y) \pmimp_{x, y} \psi(x, y)$ \\ + $\pmast11\pmcdot06$. & $\phi(x, y) \pmiff_{x, y} \psi(x, y)$ \\ + $\pmast13\pmcdot01$. & $x = y$ \\ + $\pmast13\pmcdot02$. & $x \pmnid y$ +\end{tabular} + +\begin{tabular}{l l} + $\pmast13\pmcdot03$. & $x = y = z$ \\ + $\pmast14\pmcdot01$. & $[(\pmdsc{x})(\phi x)]\pmdot \psi(\pmdsc{x})(\phi x)$ \\ + $\pmast14\pmcdot02$. & $\pmexists(\pmdsc{x})(\phi x)$ \\ + $\pmast14\pmcdot03$. & $[(\pmdsc{x})(\phi x), (\pmdsc{x})(\psi x)]\pmdot f\{(\pmdsc{x})(\phi x),$\\ + & \indent $(\pmdsc{x})(\psi x)\}$ \\ + $\pmast14\pmcdot04$. & $[(\pmdsc{x})(\psi x)]\pmdot f\{(\pmdsc{x})(\phi x), (\pmdsc{x})(\psi x)\}$ \\ + $\pmast20\pmcdot01$. & $f\{\pmcls{z}{\psi z}\}$ \\ + $\pmast20\pmcdot02$. & $x \pmcin \pmpred{\phi}{\pmhat{z}}$ \\ + $\pmast20\pmcdot03$. & $\pmsCl$ \\ + $\pmast20\pmcdot04$. & $x, y \pmcin \alpha$ \\ + $\pmast20\pmcdot05$. & $x, y, z \pmcin \alpha$ \\ + $\pmast20\pmcdot06$. & $x \pmnot \pmcin \alpha$ \\ + $\pmast20\pmcdot07$. & $(\pmall{\alpha})\pmdot f\alpha$ \\ + $\pmast20\pmcdot071$. & $(\pmsome{\alpha})\pmdot f\alpha$ \\ + $\pmast20\pmcdot072$. & $[(\pmdsc{\alpha})(\phi \alpha)]\pmdot f(\pmdsc{\alpha})(\phi \alpha)$ \\ + $\pmast20\pmcdot08$. & $f\{\pmcls{\alpha}{\psi \alpha}\}$ \\ + $\pmast20\pmcdot081$. & $\alpha \pmcin \pmpred{\psi}{\pmhat{z}}$ \\ + $\pmast21\pmcdot01$. & $f\{\pmrel{x}{y}{\phi(x,y)}\}$ \\ + $\pmast21\pmcdot02$. & $\pmrelep{a}{\pmpredd{\phi}{\pmhat{x}}{\pmhat{y}}}{b}$ \\ + $\pmast21\pmcdot03$. & $\pmRel$ \\ + $\pmast21\pmcdot07$. & $(\pmall{R})\pmdot fR$ \\ + $\pmast21\pmcdot071$. & $(\pmsome{R})\pmdot fR$ \\ + $\pmast21\pmcdot072$. & $[(\pmdsc{R})(\phi R)]\pmdot f(\pmdsc{R})(\phi R)$ \\ + $\pmast21\pmcdot08$. & $f\{\pmrel{R}{S}{\psi(R, S}\}$ \\ + $\pmast21\pmcdot081$. & $\pmrelep{P}{\pmpredd{\phi}{\pmhat{R}}{\pmhat{S}}}{Q}$ \\ + $\pmast21\pmcdot082$. & $f\{\pmcls{R}{\psi R}\}$ \\ + $\pmast21\pmcdot083$. & $R \pmcin \pmpred{\psi}{\pmhat{R}}$ \\ + $\pmast22\pmcdot01$. & $\alpha \pmcin \beta$ \\ + $\pmast22\pmcdot02$. & $\alpha \pmccap \beta$ +\end{tabular} + +\begin{tabular}{l l} +$\pmast22\pmcdot03$. & $\alpha \pmccup \beta$ \\ +$\pmast22\pmcdot04$. & $\pmccmp{\alpha}$ \\ +$\pmast22\pmcdot05$. & $\pmcmin{\alpha}{\beta}$ \\ +$\pmast22\pmcdot53$. & $\alpha \pmccap \beta \pmccap \gamma$ \\ +$\pmast22\pmcdot71$. & $\alpha \pmccup \beta \pmccup \gamma$ \\ +$\pmast23\pmcdot01$. & $R \pmrinc S$ \\ +$\pmast23\pmcdot02$. & $R \pmrcap S$ \\ +$\pmast23\pmcdot03$. & $R \pmrcup S$ \\ +$\pmast23\pmcdot04$. & $\pmrcmp{R}$ \\ +$\pmast23\pmcdot05$. & $\pmrmin{R}{S}$ \\ +$\pmast23\pmcdot53$. & $R \pmrcap S \pmrcap T$ \\ +$\pmast23\pmcdot71$. & $R \pmrcup S \pmrcup T$ \\ +$\pmast24\pmcdot01$. & $\pmcuni$ \\ +$\pmast24\pmcdot02$. & $\pmcnull$ \\ +$\pmast24\pmcdot03$. & $\pmcexists \alpha$ \\ +$\pmast25\pmcdot01$. & $\pmruni$ \\ +$\pmast25\pmcdot02$. & $\pmrnull$ \\ +$\pmast25\pmcdot03$. & $\pmrexists R$ \\ +$\pmast30\pmcdot01$. & $\pmdscf{R}{y}$ \\ +$\pmast30\pmcdot02$. & $\pmdscf{R}{\pmdscf{S}{y}}$ \\ +$\pmast31\pmcdot01$. & $\pmCnv$ \\ +$\pmast31\pmcdot02$. & $\pmcnv{P}$ \\ +$\pmast32\pmcdot01$. & $\pmRrf{R}$ \\ +$\pmast32\pmcdot02$. & $\pmRrl{R}$ \\ +$\pmast32\pmcdot03$. & $\pmsg$ \\ +$\pmast32\pmcdot04$. & $\pmgs$ \\ +$\pmast33\pmcdot01$. & $\pmDm$ \\ +$\pmast33\pmcdot02$. & $\pmCdm$ \\ +$\pmast33\pmcdot03$. & $\pmCmp$ \\ +$\pmast33\pmcdot04$. & $\pmFld$ \\ +$\pmast34\pmcdot01$. & $\pmrprd{R}{S}$ \\ +$\pmast34\pmcdot02$. & $\pmrprdn{R}{2}$ +\end{tabular} + +\begin{tabular}{l l} +$\pmast34\pmcdot03$. & $\pmrprdn{R}{3}$ \\ +$\pmast35\pmcdot01$. & $\pmrld{\alpha}{R}$ \\ +$\pmast35\pmcdot02$. & $\pmrlcd{R}{\beta}$ \\ +$\pmast35\pmcdot03$. & $\pmrlf{\alpha}{R}{\beta}$ \\ +$\pmast35\pmcdot04$. & $\pmrl{\alpha}{\beta}$ \\ +$\pmast35\pmcdot05$. & $\pmrl{\pmdscf{R}{x}}{\beta}$ \\ +$\pmast35\pmcdot24$. & $\pmrld{\alpha}{\pmrprd{R}{S}}$ \\ +$\pmast35\pmcdot25$. & $\pmrlF{P}{\alpha}$ \\ +$\pmast36\pmcdot01$. & $\pmrlf{R}{\beta}$ \\ +$\pmast37\pmcdot01$. & $\pmdscf{R}{\beta}$ \\ +$\pmast37\pmcdot02$. & $\pmdscfR{R}$ \\ +$\pmast37\pmcdot03$. & $\pmcnv{\pmdscfR{R}}$\\ +$\pmast37\pmcdot04$. & $\pmdscfff{R}{\kappa}$ \\ +$\pmast37\pmcdot05$. & $\pmdscfe{R}{\beta}$ \\ +$\pmast38\pmcdot01$. & $x \pmop$ \\ +$\pmast38\pmcdot02$. & $\pmop x$ \\ +$\pmast38\pmcdot03$. & $\pmopc{\alpha}{y}$\\ +$\pmast40\pmcdot01$. & $\pmccsum{\kappa}$ \\ +$\pmast40\pmcdot02$. & $\pmccprd{\kappa}$ \\ +$\pmast41\pmcdot01$. & $\pmcrsum{\lambda}$ \\ +$\pmast41\pmcdot02$. & $\pmcrprd{\lambda}$ \\ +$\pmast43\pmcdot01$. & $\pmrprdd{R}{S}$ \\ +$\pmast50\pmcdot01$. & $\pmrid$ \\ +$\pmast50\pmcdot02$. & $\pmrdiv$ \\ +$\pmast51\pmcdot01$. & $\pmcUnit$ \\ +$\pmast52\pmcdot01$. & $\pmcn{1}$ \\ +$\pmast54\pmcdot01$. & $\pmcn{0}$ \\ +$\pmast54\pmcdot02$. & $\pmcn{2}$ \\ +$\pmast55\pmcdot01$. & $\pmoc{x}{y}$ \\ +$\pmast55\pmcdot02$. & $\pmoc{\pmdscf{R}{x}}{y}$ \\ +$\pmast56\pmcdot01$. & $\pmdn{2}$ \\ +$\pmast56\pmcdot02$. & $\pmrn{2}$ +\end{tabular} + +\begin{tabular}{l l} +$\pmast56\pmcdot03$. & $\pmrn{0}$ \\ +$\pmast60\pmcdot01$. & $\pmsCl$ \\ +$\pmast60\pmcdot02$. & $\pmsCle$ \\ +$\pmast60\pmcdot03$. & $\pmClsn{2}$ \\ +$\pmast60\pmcdot04$. & $\pmClsn{3}$ \\ +$\pmast61\pmcdot01$. & $\pmsRl$ \\ +$\pmast61\pmcdot02$. & $\pmsRle$ \\ +$\pmast61\pmcdot03$. & $\pmReln{2}$ \\ +$\pmast61\pmcdot04$. & $\pmReln{3}$ \\ +$\pmast62\pmcdot01$. & $\pmrin$ \\ +$\pmast63\pmcdot01$. & $\pmrt{x}$ \\ +$\pmast63\pmcdot011$. & $\pmrtc{1}{x}$ \\ +$\pmast63\pmcdot02$. & $\pmrti{0}{\alpha}$ \\ +$\pmast63\pmcdot03$. & $\pmrti{1}{\kappa}$ \\ +$\pmast63\pmcdot04$. & $\pmrtc{2}{\kappa}$ \\ +$\pmast63\pmcdot041$. & $\pmrtc{3}{\kappa}$ \\ +$\pmast63\pmcdot05$. & $\pmrti{2}{\kappa}$ \\ +$\pmast63\pmcdot051$. & $\pmrti{3}{\kappa}$ \\ +$\pmast64\pmcdot01$. & $\pmrtri{00}{\alpha}$ \\ +$\pmast64\pmcdot011$. & $\pmrtrc{11}{x}$ \\ +$\pmast64\pmcdot012$. & $\pmrtc{12}{x}$ \\ +$\pmast64\pmcdot013$. & $\pmrtc{21}{x}$ \\ +$\pmast64\pmcdot014$. & $\pmrtc{22}{x}$ \\ +$\pmast64\pmcdot02$. & $\pmrti{01}{\alpha}$ \\ +$\pmast64\pmcdot021$. & $\pmrti{10}{\alpha}$ \\ +$\pmast64\pmcdot022$. & $\pmrti{11}{\alpha}$ \\ +$\pmast64\pmcdot03$. & $\pmrtric{0}{1}{\alpha}$ \\ +$\pmast64\pmcdot031$. & $\pmrtric{1}{1}{\alpha}$ \\ +$\pmast64\pmcdot04$. & $\pmrtrci{1}{0}{\alpha}$ \\ +$\pmast64\pmcdot041$. & $\pmrtrci{1}{1}{\alpha}$ \\ +$\pmast65\pmcdot01$. & $\pmrtdi{\alpha}{x}$ \\ +$\pmast65\pmcdot02$. & $\pmrtdc{\alpha}{x}$ +\end{tabular} + +\begin{tabular}{l l} +$\pmast65\pmcdot03$. & $\pmrtdri{R}{x}$ \\ +$\pmast65\pmcdot04$. & $\pmrtdrc{R}{x}$ \\ +$\pmast65\pmcdot1$. & $\pmrtdri{R}{(x,y)}$ \\ +$\pmast65\pmcdot11$. & $\pmrtdrc{R}{x_y}$\\ +$\pmast65\pmcdot12$. & $\pmrtdrc{R}{x, y}$ \\ +$\pmast70\pmcdot01$. & $\pmrdc{\alpha}{\beta}$ \\ +$\pmast73\pmcdot01$. & $\alpha \pmsmbar \beta$ \\ +$\pmast73\pmcdot02$. & $\pmsm$\\ +$\pmast80\pmcdot01$. & $\pmSelp$ \\ +$\pmast84\pmcdot01$. & $\pmexc$ \\ +$\pmast84\pmcdot02$. & $\pmexcc{\gamma}$ \\ +$\pmast84\pmcdot03$. & $\pmexcn$\\ +$\pmast85\pmcdot5$. & $\pmselc{P}{y}$ \\ +$\pmast88\pmcdot01$. & $\pmmultr$ \\ +$\pmast88\pmcdot02$. & $\pmmultc$ \\ +$\pmast88\pmcdot03$. & $\pmmultax$ \\ +$\pmast90\pmcdot01$. & $\pmanc{R}$ \\ +$\pmast90\pmcdot02$. & $\pmancc{R}$ \\ +$\pmast91\pmcdot01$. & $\pmrst{R}$ \\ +$\pmast91\pmcdot02$. & $\pmrts{R}$ \\ +$\pmast91\pmcdot03$. & $\pmpot{R}$ \\ +$\pmast91\pmcdot04$. & $\pmpotid{R}$ \\ +$\pmast91\pmcdot05$. & $\pmpo{R}$ \\ +$\pmast93\pmcdot01$. & $\pmB$ \\ +$\pmast93\pmcdot02$. & $\pmmin{P}$ \\ +$\pmast93\pmcdot021$. & $\pmmax{P}$ \\ +$\pmast93\pmcdot03$. & $\pmgen{P}$ \\ +$\pmast95\pmcdot01$. & $\pmefr{P}{Q}$ \\ +$\pmast96\pmcdot01$. & $\pmipr{R}{x}$ \\ +$\pmast96\pmcdot02$. & $\pmjpr{R}{x}$ \\ +$\pmast97\pmcdot01$. & $\pmfr{R}{x}$ \\ +$\pmast100\pmcdot01$. & $\pmNc$ +\end{tabular} + +\end{document} \ No newline at end of file diff --git a/principia.sty b/principia.sty index 33010b4..0ceafab 100644 --- a/principia.sty +++ b/principia.sty @@ -15,14 +15,26 @@ %Meta-logical symbols \newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof. +\newcommand{\pmdemi}{\indent \pmdem} %This idents the notation that begins a proof. +\newcommand{\pmprop}{\text{Prop}} %This occurs at the end of a proof. +\newcommand{\pmithm}{\pmimp\;\pmthm} %This occurs when a meta-theoretic implication is asserted. +\newcommand{\pmbr}[1]{\bigg \lbrack \normalsize #1 \bigg \rbrack} %These are larger brackets for substitution. \newcommand{\pmsub}[2]{\bigg \lbrack \small \begin{array}{c} #1 \\ \hline #2 \end{array} \bigg \rbrack} %This is the substitution command. -\newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmsubb}[4]{\bigg \lbrack \small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array} \bigg \rbrack} %This is the substitution command. -\newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmsubbb}[6]{\bigg \lbrack \small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array} \bigg \rbrack} %This is the substitution command. -\newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmsubbbb}[8]{\bigg \lbrack \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command. -\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmsUb}[2]{\small \begin{array}{c} #1 \\ \hline #2 \end{array}} %This is the substitution command. +\newcommand{\pmsUbb}[4]{\small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}} %This is the substitution command. +\newcommand{\pmsUbbb}[6]{\small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}} %This is the substitution command. +\newcommand{\pmsUbbbb}[8]{\small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command. +\newcommand{\pmSUb}[3]{\normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}} %This is the substitution command. +\newcommand{\pmSUbb}[5]{\normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}} %This is the substitution command. +\newcommand{\pmSUbbb}[7]{\normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}} %This is the substitution command. +\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command. \newcommand{\pmthm}{\mathpunct{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}}} %This is the theorem sign. \newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number. \newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol\cdot$}}} %This is a sign introducing a theorem sub-number. @@ -198,9 +210,10 @@ \newcommand{\pmSele}{\pmcin_{\Delta}} \newcommand{\pmself}[1]{F_{\small\Delta}\mathbf{`}#1} \newcommand{\pmSelf}{F_{\Delta}} +\newcommand{\pmex}[1]{\text{Cls} \mathop{\text{excl}}\mathbf{`}#1} \newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}} \newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1} -\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}}^2 \mathop{\text{excl}}} +\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}^2} \mathop{\text{excl}}} \newcommand{\pmselc}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\boldsymbol{\mapsto}$}} #2} \newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}} \newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}} @@ -231,4 +244,9 @@ \newcommand{\pmNc}{\text{Nc}} \newcommand{\pmNC}{\text{NC}} \newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1} -\newcommand{\pmNoc}{\text{N}_0\text{c}} \ No newline at end of file +\newcommand{\pmNoc}{\text{N}_0\text{c}} +\newcommand{\pmnocind}[1]{\text{N}_0\text{Cinduct}\textbf{`}#1} +\newcommand{\pmNocind}{\text{N}_0\text{Cinduct}} + +\newcommand{\pmclsrefl}{\text{Cls} \mathop{\text{refl}}} +\newcommand{\pmncrefl}{\text{NC} \mathop{\text{refl}}} \ No newline at end of file -- cgit v1.2.3