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Results tagged with lo.logic
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user 4241
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.
32
votes
Is all ordinary mathematics contained in high school mathematics?
The statement that the periodicity of Laver tables tends to infinity is not provable in PRA (hence also EFA), although it is provable under the assumption of a rank-into-rank embedding.
- 884
11
votes
Why are proofs so valuable, although we do not know that our axiom system is consistent?
We adopt axioms not because we can prove their consistency, but because we believe that they accurately describe something that we want to study. A proof from these axioms will have value in that it …
9
votes
1
answer
547
views
Forcing to "minimally" add new reals.
Suppose that I want to force to add a "single" new subset of $\omega$ and not much else. For example, consider the Cohen forcing consisting of finite partial functions from $\omega$ to 2. The forcing …
- 884
7
votes
1
answer
2k
views
Least ordinal not in a countable transitive model of ZFC
Frequently it is useful do deal with countable transitive models M of ZFC, for example in forcing constructions.
The notion of being an ordinal is absolute for any transitive model, so certainly if …
- 884