Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic

Mykyta Narusevych

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arXiv · 2606.01163

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic

Mykyta Narusevych

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Abstract

We formulate a factorization hypothesis for linear orders definable by oracle polynomial-time machines. Assuming this hypothesis, we provide an approach to constructing a nonstandard model satisfying the minimization scheme for polynomial-time predicates while violating the tournament principle for graphs with polynomial-time edge relation.

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Mykyta Narusevych. 2026-05-31. Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic. https://arxiv.org/abs/2606.01163

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