Aug 21, 2021 · Decidable means there is a Turing-machine that accepts all and only instances of that language, but also explicitly rejects when input is not that language. So, this Turing-machine will …

Aug 28, 2019 · So whether a theory T is decidable is an epistemological fact. A statement about what we can effectively know, but completeness is a metaphysical fact about the theory.

Mar 8, 2011 · What is difference between "recognizable" and "decidable" in context of Turing machines?

Dec 26, 2020 · Let's say checking if a proof is valid is decidable. Then surely we can just enumerate the proofs then check if it's valid. This seems to be a semi-decidable procedure. But why …

Oct 14, 2023 · See e.g. Enderton's Logic, page 142-145 for decidability: "Let $\Gamma$ be a decidable set of formulas in a reasonable language. Then, the set of theorems of $\Gamma$ is effectively …

Jun 17, 2015 · If satisfiability were semi-decidable, then satisfiability and its complement, unsatisfiability would both be semi-decidable, so satisfiability would be decidable, in which case validity would be …

Apr 9, 2021 · We know that a set is decidable iff the set and its complement are both semi-decidable. Thus, the undecidability of validity implies that the complement of the set of valid formulas is not semi …

May 29, 2012 · It seems very confusing that real closed field (which also can be used as the theory of real number) is decidable, while Peano arithmetic, which seems to be a subset of real closed field is …

Apr 16, 2024 · How to prove that the union of two semi decidable languages ist semi decidable. Ask Question Asked 3 years, 7 months ago Modified 1 year, 10 months ago

Jan 4, 2022 · I know very little about modal logic (only some set theory) in mathematics, but I am aware that there exists a completeness theorem, incompleteness theorem, and the axiom choice, and that …