Geodesic
On decidability of finite subsets’ theory for discrete linear order
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2022), pp. 91-104

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Let us consider a discrete linear ordered set. On finite subsets of such set we introduce a new binary relation. This relation says that all items of a first set is less than all items of a second one. We show that the theory of such constructed structure admits quantifier elimination. For this purpose, we expand the language with four definable functions. As a corollary we get the theory of finite subsets of a discrete linear order to be decidable.
Keywords: theory, finite subsets, discrete linear order, decidability.
Mots-clés : quantifiers elimination 
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     author = {N. V. Avkhimovich},
     title = {On decidability of finite subsets{\textquoteright} theory for discrete linear order},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {91--104},
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     year = {2022},
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N. V. Avkhimovich. On decidability of finite subsets’ theory for discrete linear order. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2022), pp. 91-104. http://geodesic.mathdoc.fr/item/VTPMK_2022_3_a6/