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  1. The strength of extensionality II—weak weak set theories without infinity.Kentaro Sato - 2011 - Annals of Pure and Applied Logic 162 (8):579-646.
    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 (...)
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