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arXiv · 2209.01197

Models of $VTC^0$ as exponential integer parts

Emil Jeřábek
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Abstract

We prove that (additive) ordered group reducts of nonstandard models of the bounded arithmetical theory $\mathsf{VTC^0}$ are recursively saturated in a rich language with predicates expressing the integers, rationals, and logarithmically bounded numbers. Combined with our previous results on the construction of the real exponential function on completions of models of $\mathsf{VTC^0}$, we show that every countable model of $\mathsf{VTC^0}$ is an exponential integer part of a real-closed exponential field.

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Emil Jeřábek. 2022-09-02. Models of $VTC^0$ as exponential integer parts. https://doi.org/10.1002/malq.202300001

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