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| author | Tanaka Akira | 2019-02-01 11:00:19 +0900 |
|---|---|---|
| committer | Tanaka Akira | 2019-02-01 11:00:19 +0900 |
| commit | 162101e6bc5b3bb33b741ff51e37805ffd624d0d (patch) | |
| tree | b991010d4c6e75e0a82579c57c7d22f7a5be0557 /dev | |
| parent | f6f9cf742ee5894be65d6e2de527e3ab5a643491 (diff) | |
The lowest universe level is 1.
Cic description doesn't describe the lowest universe level clearly.
- "Type(i) for any integer i" seems Type(-1) is possible
- "S = {Prop,Set,Type(i)| i ∈ ℕ }" depends on the definition of "ℕ"
which is not described.
It is well known that there are two definitions that ℕ includes 0 or not.
In Coq, it is natural that ℕ includes 0 because the inductive type
nat includes 0.
- "Prop:Type(1), Set:Type(1)" suggests the lowest level is 1.
- AX-Prop and AX-Set describes Prop:Type(1) and Set:Type(1).
So, Prop and Set are not belongs to Type(0).
Also, CPDT describes that "The type of Set is Type(0)".
http://adam.chlipala.net/cpdt/html/Universes.html
I think the lowest universe level is 1 because AX-Prop and AX-Set.
I'm not certain to fix this problem but
my idea to fix this problem is changing
"Type(i) for any integer i" to
"Type(i) for any integer i ≥ 1".
Diffstat (limited to 'dev')
0 files changed, 0 insertions, 0 deletions
