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Proving consistency of equational theories in bounded arithmetic

File: PDF-File

Author: Arnold Beckmann
Title: Proving consistency of equational theories in bounded arithmetic
Journal: JSL 2002, 67(1): 279-296

Abstract: We consider equational theories for functions defined via recursion involving equations between closed terms with natural rules based on recursive definition of the function symbols. We show that consistency of such equational theories can be proved in the weak fragment of arithmetic S 1 2 . In particular this solves an open problem formulated by Takeuti.

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