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On proving consistency of equational theories in Bounded Arithmetic

Arnold Beckmann and Yoriyuki Yamagata
submitted for publication
Publication year: 2022

We consider pure equational theories that allow substitution but disallow induction, which we denote as PETS, based on recursive definition of their function symbols. We show that the Bounded Arithmetic theory S12 proves the consistency of PETS. Our approach employs models for PETS based on approximate values resembling notions from domain theory in Bounded Arithmetic, which may be of independent interest.