Definability in terms of the successor function and the coprimeness predicate in the set of arbitrary integers

Journal of Symbolic Logic 54 (4):1253-1287 (1989)
Using coding devices based on a theorem due to Zsigmondy, Birkhoff and Vandiver, we first define in terms of successor S and coprimeness predicate $\perp$ a full arithmetic over the set of powers of some fixed prime, then we define in the same terms a restriction of the exponentiation. Hence we prove the main result insuring that all arithmetical relations and functions over prime powers and their opposite are $\{S, \perp\}$ -definable over Z. Applications to definability over Z and N are stated as corollaries of the main theorem
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