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On the theory of exponential integer parts (2404.06888v1)
Published 10 Apr 2024 in math.LO and cs.LO
Abstract: We axiomatize the first-order theories of exponential integer parts of real-closed exponential fields in a language with $2x$, 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.