First- and Second-Order Models of Recursive Arithmetics

Ján Kľuka; Paul J. Voda

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arXiv · 1705.05459

First- and Second-Order Models of Recursive Arithmetics

Ján Kľuka·Paul J. Voda

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Abstract

We study a quadruple of interrelated subexponential subsystems of arithmetic WKL$_0^-$, RCA$^-_0$, I$\Delta_0$, and $\Delta$RA$_1$, which complement the similarly related quadruple WKL$_0$, RCA$_0$, I$\Sigma_1$, and PRA studied by Simpson, and the quadruple WKL$_0^\ast$, RCA$_0^\ast$, I$\Delta_0$(exp), and EFA studied by Simpson and Smith. We then explore the space of subexponential arithmetic theories between I$\Delta_0$ and I$\Delta_0$(exp). We introduce and study first- and second-order theories of recursive arithmetic $A$RA$_1$ and $A$RA$_2$ capable of characterizing various computational complexity classes and based on function algebras $A$, studied by Clote and others.

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Ján Kľuka, Paul J. Voda. 2017-05-15. First- and Second-Order Models of Recursive Arithmetics. https://arxiv.org/abs/1705.05459

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