Submission date: 10 April 2024

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.

Mathematics Subject Classification: 03C62 (Primary) 03C64, 91A05 (Secondary)

Keywords and phrases:

Full text arXiv 2404.06888: pdf, ps.