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arXiv · 2404.06888

On the theory of exponential integer parts

Emil Jeřábek
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Abstract

We axiomatize the first-order theories of exponential integer parts of real-closed exponential fields in a language with $2^x$, in a language with a predicate for powers of 2, and in the basic language of ordered rings. In particular, the last theory extends IOpen by sentences expressing the existence of winning strategies in a certain game on integers; we show that it is a proper extension of IOpen, and give upper and lower bounds on the required number of rounds needed to win the game.

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Emil Jeřábek. 2024-04-10. On the theory of exponential integer parts. https://arxiv.org/abs/2404.06888

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