Elementary function arithmetic: Difference between revisions

Revision as of 23:28, 21 October 2010

Revision as of 23:29, 21 October 2010

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In [[proof theory]], a branch of [[mathematical logic]], '''elementary function arithmetic''' or '''exponential function arithmetic''' or '''(EFA)''' is the system of arithmetic with the usual elementary properties of 0, 1, +, ×, ''x''^''y'', together with [[mathematical induction|induction]] for formulas with bounded quantifiers.

EFA is a very weak logical system, whose [[proof theoretic ordinal]] is ω³, but still seems able to prove much of ordinary mathematics that can be stated in the language of first-order arithmetic.