Geodesic
Collapse Result for Extensions of the Presburger Arithmetic by a~Unary Function Compatible with Addition
Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 362-371.

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Earlier, Belegradek, Stolboushkin, and Taitslin proved that the collapse result holds in the theory of natural numbers with addition, i.e., each locally generic query using addition can be written without it. In this paper, we use the sufficient conditions of the collapse result obtained by Taitslin to prove that it holds in any extensions of the Presburger arithmetic by a unary function compatible with addition. The notion of a function compatible with addition was proposed by A. L. Semenov. 
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S. M. Dudakov. Collapse Result for Extensions of the Presburger Arithmetic by a~Unary Function Compatible with Addition. Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 362-371. http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a5/

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