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A wild model of linear arithmetic and discretely ordered modules
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SYSNO ASEP 0484738 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název A wild model of linear arithmetic and discretely ordered modules Tvůrce(i) Glivický, Petr (MU-W) SAI, ORCID
Pudlák, Pavel (MU-W) RID, SAIZdroj.dok. Mathematical Logic Quarterly. - : Wiley - ISSN 0942-5616
Roč. 63, č. 6 (2017), s. 501-508Poč.str. 8 s. Jazyk dok. eng - angličtina Země vyd. DE - Německo Klíč. slova linear arithmetics Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics Institucionální podpora MU-W - RVO:67985840 UT WOS 000419821500003 EID SCOPUS 85038242375 DOI 10.1002/malq.201600012 Anotace Linear arithmetics are extensions of Presburger arithmetic (Pr) by one or more unary functions, each intended as multiplication by a fixed element (scalar), and containing the full induction schemes for their respective languages. In this paper, we construct a model M of the 2-linear arithmetic LA2 (linear arithmetic with two scalars) in which an infinitely long initial segment of Peano multiplication on M is phi-definable. This shows, in particular, that LA2 is not model complete in contrast to theories LA1 and LA0=Pr that are known to satisfy quantifier elimination up to disjunctions of primitive positive formulas. As an application, we show that M, as a discretely ordered module over the discretely ordered ring generated by the two scalars, does not have the NIP, answering negatively a question of Chernikov and Hils. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2018
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