On proving consistency of equational theories in Bounded Arithmetic

03/09/2022

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by   Arnold Beckmann, et al.

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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 S^1_2 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.