David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Symbolic Logic 67 (1):279-296 (2002)
We consider equational theories for functions defined via recursion involving equations between closed terms with natural rules based on recursive definitions 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 (c.f. [5, p.5 problem 9.])
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Arnold Beckmann (2004). Preservation Theorems and Restricted Consistency Statements in Bounded Arithmetic. Annals of Pure and Applied Logic 126 (1-3):255-280.
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