The strength of extensionality II - Weak weak set theories without infinity

作者：Sato Kentaro^*

来源：Annals of Pure and Applied Logic, 2011, 162(8): 579-646.

DOI：10.1016/j.apal.2010.11.001

• Finite set theory
• Graphic conception of sets
• Bounded reverse mathematics
• Provably total functions
• Subtheories of V(0)
• Complexities below P

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 (2009) 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.

• 出版日期2011-8