Proof of incompleteness theorem via derivability conditions #1
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
SnO2WMaN
force-pushed
the
provability
branch
4 times, most recently
from
07a1657 to
18b3d19
Compare
SnO2WMaN
force-pushed
the
provability
branch
2 times, most recently
from
bcf6845 to
8ea471c
Compare
SnO2WMaN
commented
Dec 6, 2023
Comment on lines
+30
to
+33
| have : Subtheory T₀ (T ∪ {~σ}) := by sorry; | ||
| have : Derivability1 T₀ (T ∪ {~σ}) := by sorry; | ||
| have : Derivability2 T₀ (T ∪ {~σ}) := by sorry; | ||
| have : Derivability3 T₀ (T ∪ {~σ}) := by sorry; |
SnO2WMaN
commented
Dec 6, 2023
There was a problem hiding this comment.
PropositionalCalculusの部分はLogic.Logic.HilbertStyleに移してもいいと思う
SnO2WMaN
commented
Dec 6, 2023
Comment on lines
147
to
148
| lemma existsKreiselSentence [hdef : Definable.Sigma T n] (σ) | ||
| : ∃ (K : Sentence ℒₒᵣ), IsKrieselSentence T₀ T K σ := by sorry |
There was a problem hiding this comment.
Löbの定理を第2不完全性定理を用いずに示すためにこの補題が必要だが，代入に関する問題（Subsentenceの束縛されていない変数の数が合わない？）で上手く出来なかった記憶がある
SnO2WMaN
force-pushed
the
provability
branch
from
e7fd1bc to
b65c042
Compare
|
HilbertStyleの補題を使っている証明をhttps://github.com/iehality/lean4-logic/blob/master/Logic/AutoProver/Prover.lean の |
SnO2WMaN
force-pushed
the
provability
branch
from
f3bc207 to
cb0e36b
Compare
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
No description provided.