On Lattices of Regular Sets of Natural Integers Closed under Decrementation

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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Source https://hal.science/hal-00870130
Author Cegielski, Patrick, Grigorieff, Serge, Guessarian, Irene
Maintainer CCSD
Last Updated May 9, 2026, 11:32 (UTC)
Created May 9, 2026, 11:32 (UTC)
Identifier hal-00870130
Language en
contributor Laboratoire d'Algorithmique Complexité et Logique (LACL) ; Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)
creator Cegielski, Patrick
date 2013-02-25T00:00:00
harvest_object_id 270c6818-d459-4914-ad61-5e2c4abc6009
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2024-12-27T00:00:00
relation info:eu-repo/semantics/altIdentifier/arxiv/submit/0816591
set_spec type:UNDEFINED