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Results tagged with lo.logic
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user 66044
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
10
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0
answers
197
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4-quantifier formula not decided by ZF
This interesting question asks the minimum number of quantifiers required to state the Axiom of Choice, and recalls that any sentence having three or fewer quantifiers is already decided by ZF. This a …
- 1,124
7
votes
1
answer
753
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Are there any recent advances in formalizing the undecidability of $\mathit{CH}$?
The website Formalizing 100 Theorems by Freek Wiedijk contains a list of some theorems that were chosen at some point as good candidates for formalization (because of their complexity, their importanc …
- 4,713
4
votes
1
answer
383
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Consistency strength of weakly inaccessibles without $\mathsf{GCH}$
This is a revised version of a post on Math.SE. It is a rather basic question (which I'd be glad to delete if the community regards as off-topic).
Is there a way to prove that (if consistent) $\mat …
- 14.1k
10
votes
1
answer
534
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Looking for “Set theory for a small universe” by Ketonen
In the paper Partition theorems for systems of finite subsets of integers, Pudlák and Rödl show a Ramsey-type result. The main feature of this result is that the sizes of sets in such systems are not …
- 1,228
13
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0
answers
342
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Can you define a probability measure on the set of countable transitive models of ZFC?
It is well known that the set of hereditarily countable sets $H(\omega_1)$ —or, if you prefer, $H_{\omega_1}$— has cardinality $2^{\aleph_0}$, and I understand that every countable transitive model ( …
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- 1