Proving consistency of equational theories in bounded arithmetic
Arnold Beckmann · Journal of Symbolic Logic · 2002
Abstract We consider equational theories for functions denned 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 S21. In particular this solves an open problem formulated by Takeuti (c.f. [5, p.5 problem 9.]).