Elementary function arithmetic: Difference between revisions

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{{Short description|System of arithmetic in proof theory}}

{{No footnotes|date=November 2017}}

{{redirect|Elementary recursive arithmetic|the computational complexity class|ELEMENTARYElementary recursive function}}

In [[proof theory]], a branch of [[mathematical logic]], '''elementary function arithmetic''' ('''EFA'''), also called '''elementary arithmetic''' and '''exponential function arithmetic''',<ref>C. Smoryński, "Nonstandard Models and Related Developments" (p. 217). From ''Harvey Friedman's Research on the Foundations of Mathematics'' (1985), Studies in Logic and the Foundations of Mathematics vol. 117.</ref> is the system of arithmetic with the usual elementary properties of 0,&nbsp;1,&nbsp;+,&nbsp;×,&nbsp;<math>x^y</math>, together with [[mathematical induction|induction]] for formulas with [[bounded quantifier]]s.