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arXiv · 1310.1378

On Lattices of Regular Sets of Natural Integers Closed under Decrementation

Patrick Cégielski·Serge Grigorieff·Irène Guessarian
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Abstract

We consider lattices of regular sets of non negative integers, i.e. of sets definable in Presbuger arithmetic. We prove that if such a lattice is closed under decrement then it is also closed under many other functions: quotients by an integer, roots, etc.

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Patrick Cégielski, Serge Grigorieff, Irène Guessarian. 2013-10-04. On Lattices of Regular Sets of Natural Integers Closed under Decrementation. https://arxiv.org/abs/1310.1378

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