The strength of extensionality II—weak weak set theories without infinity

Annals of Pure and Applied Logic 162 (8):579-646 (2011)
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Abstract

By obtaining several new results on Cook-style two-sorted bounded arithmetic, this paper measures the strengths of the axiom of extensionality and of other weak fundamental set-theoretic axioms in the absence of the axiom of infinity, following the author’s previous work [K. Sato, The strength of extensionality I — weak weak set theories with infinity, Annals of Pure and Applied Logic 157 234–268] which measures them in the presence. These investigations provide a uniform framework in which three different kinds of reverse mathematics–Friedman–Simpson’s “orthodox” reverse mathematics, Cook’s bounded reverse mathematics and large cardinal theory–can be reformulated within one language so that we can compare them more directly

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References found in this work

Notes on polynomially bounded arithmetic.Domenico Zambella - 1996 - Journal of Symbolic Logic 61 (3):942-966.
Factorization of polynomials and °1 induction.S. G. Simpson - 1986 - Annals of Pure and Applied Logic 31:289.
On Interpretations of Arithmetic and Set Theory.Richard Kaye & Tin Lok Wong - 2007 - Notre Dame Journal of Formal Logic 48 (4):497-510.
Interpreting classical theories in constructive ones.Jeremy Avigad - 2000 - Journal of Symbolic Logic 65 (4):1785-1812.

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