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Results tagged with lo.logic
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user 101968
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.
1
vote
Can a universal induction rule be formulated?
My question is, is there a way to formalize this universal induction principle?
How about the (infinitary) Hilbert $\omega$-rule:
$$P(1), P(2), P(3), \cdots\over \forall n P(n) $$
Not sure if t …
- 11
-1
votes
Are there any natural theories T for which P=NP implies T proves P=NP?
Does this work? Use the Bellantoni-Cook theorem to enumerate all the polynomial time Turing machines. If P=NP you will eventually run into a machine that you can recognize as running Levin's universa …
- 11