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<p>We study reflexivity (the ability of a theory to prove a certain consistency statement for finitely axiomatizable sub-theories) of consistency statements similar to <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-consistency. We address and generalize, besides the usual <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-consistency, <i>n</i>-consistency, a uniform version of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-consistency, and a consistency statement that expresses that a theory does not refute full induction.</p>

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Reflexivity of \(\omega \)-Consistency in a General Setting

  • 期刊论文

  • 发表日期：

    2025年10月31日

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  • Paulo Guilherme Santos

摘要

We study reflexivity (the ability of a theory to prove a certain consistency statement for finitely axiomatizable sub-theories) of consistency statements similar to \(\omega \) ω -consistency. We address and generalize, besides the usual \(\omega \) ω -consistency, n-consistency, a uniform version of \(\omega \) ω -consistency, and a consistency statement that expresses that a theory does not refute full induction.