On the theory of exponential integer parts
<|reference_start|>On the theory of exponential integer parts: 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.<|reference_end|>
@article{jeřábek2024on,
    title={On the theory of exponential integer parts},
    author={Emil Jev{r}'abek},
    journal={arXiv preprint arXiv:2404.06888},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.06888},
    primaryClass={math.LO cs.LO}
}