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Results tagged with lo.logic
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user 2757
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.
46
votes
15
answers
11k
views
Strong induction without a base case
Strong induction proves a sequence of statements $P(0)$, $P(1)$, $\ldots$ by proving the implication
"If $P(m)$ is true for all nonnegative integers $m$ less than $n$, then $P(n)$ is true."
for ev …
- 8,842
13
votes
Which finitely presented groups can be distinguished by decidable properties?
The isomorphism relation for finitely presented groups is c.e., and in fact is Turing equivalent to the halting problem.
Proof:
To check whether two finitely presented groups $G$ and $H$ are i …
- 23.8k
23
votes
Is the theory of categories decidable?
This answer builds on those of F. G. Dorais and Joel David Hamkins to answer your "specific question", the question left open by them, namely whether the theory of abelian categories is decidable.
Th …
- 23.8k