 Omega-consistency of an arithmetic theory (source code)

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= Omega-consistency of an arithmetic theory
{title2=$\omega\text{-consistency}$}

= Omega-consistency
{synonym}

A <first-order theory> is omega-consistent when it never proves $\exists x\phi(x)$ while proving $\neg\phi(\bar n)$ for every standard <natural number> $n$. Restricting the matrix to <arithmetic> <bounded arithmetic formulas> gives <one-consistency>. This condition concerns standard instances and is stronger tha <first-order consistency>.

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