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Results tagged with computability-theory
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user 4613
computable sets and functions, Turing degrees, c.e. degrees, models of computability, primitive recursion, oracle computation, models of computability, decision problems, undecidability, Turing jump, halting problem, notions of computable randomness, computable model theory, computable equivalence relation theory, arithmetic and hyperarithmetic hierarchy, infinitary computability, $\alpha$-recursion, complexity theory.
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Does "every" first-order theory have a finitely axiomatizable conservative extension?
I originally asked this question on math.stackexchange.com here.
There's a famous theorem (due to Montague) that states that if $\sf ZFC$ is consistent then it cannot be finitely axiomatized. Howe …
- 3,137
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Decision problems for which it is unknown whether they are decidable
In Conway's Game of Life, the problem of deciding whether a given pattern with finitely many live cells is a Garden of Eden (i.e. whether it lacks a predecessor).
The main obstacle is that there could …