7 апр. 2018 г. · Usually we use the notation TA to denote the theory of true arithmetic, meaning the theory of the standard model of arithmetic ⟨N,+,⋅,0,1,<⟩ ...

23 дек. 2022 г. · Does ACA0 + True Arithmetic prove the well-foundedness of every recursive ordinal? ... As discussed in Noah Schweber's answer to What is the proof ...

19 февр. 2015 г. · ACAT is finitely axiomatized, hence whenever it is interpretable in some theory, it is also interpretable in its finite subtheory.

5 июл. 2020 г. · As long as the translation τ is computable (or even arithmetical) this isn't possible. For any arithmetical τ and recursively axiomatizable T ...

28 авг. 2024 г. · Suppose that ZF is inconsistent in your model, then adding more axioms won't solve that problem, and so ZF+TA is just as inconsistent.

18 окт. 2016 г. · There can be no such theory T, even if you weaken the requirement to T being merely arithmetically definable, rather than insisting it must ...

16 сент. 2019 г. · What you've written is a bit unclear. If you do not extend the ZFC schemes to formulas involving the new signature, then the answer is yes: ...

27 авг. 2024 г. · The answer is yes. I believe the following is best attributed to Feferman 1960; more generally, look up "arithmetized completeness theorem".

1 окт. 2023 г. · Analogous to the model of True Arithmetic, the model of "True Computation" is defined to be the set of all true first-order statements about ...

25 авг. 2020 г. · The set of models of true arithmetic is indeed ΠΠ0ω-complete under Wadge reducibility. That is, for any ΠΠ0ω set X on a Polish space Y, ...