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- W4311134489 abstract "Abstract We employ the lens provided by formal truth theory to study axiomatizations of Peano Arithmetic ${textsf {(PA)}}$ . More specifically, let Elementary Arithmetic ${textsf {(EA)}}$ be the fragment $mathsf {I}Delta _0 + mathsf {Exp}$ of ${textsf {PA}}$ , and let ${textsf {CT}}^-[{textsf {EA}}]$ be the extension of ${textsf {EA}}$ by the commonly studied axioms of compositional truth ${textsf {CT}}^-$ . We investigate both local and global properties of the family of first order theories of the form ${textsf {CT}}^-[{textsf {EA}}] +alpha $ , where $alpha $ is a particular way of expressing “ ${textsf {PA}}$ is true” (using the truth predicate). Our focus is dominantly on two types of axiomatizations, namely: (1) schematic axiomatizations that are deductively equivalent to ${textsf {PA}}$ and (2) axiomatizations that are proof-theoretically equivalent to the canonical axiomatization of ${textsf {PA}}$ ." @default.
- W4311134489 created "2022-12-23" @default.
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- W4311134489 date "2022-12-12" @default.
- W4311134489 modified "2023-10-18" @default.
- W4311134489 title "AXIOMATIZATIONS OF PEANO ARITHMETIC: A TRUTH-THEORETIC VIEW" @default.
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- W4311134489 doi "https://doi.org/10.1017/jsl.2022.83" @default.
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