A wild model of linear arithmetic and discretely ordered modules
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00484738" target="_blank" >RIV/67985840:_____/17:00484738 - isvavai.cz</a>
Alternative codes found
RIV/61384399:31140/17:00051531
Result on the web
<a href="http://dx.doi.org/10.1002/malq.201600012" target="_blank" >http://dx.doi.org/10.1002/malq.201600012</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/malq.201600012" target="_blank" >10.1002/malq.201600012</a>
Alternative languages
Result language
angličtina
Original language name
A wild model of linear arithmetic and discretely ordered modules
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Logic Quarterly
ISSN
0942-5616
e-ISSN
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Volume of the periodical
63
Issue of the periodical within the volume
6
Country of publishing house
DE - GERMANY
Number of pages
8
Pages from-to
501-508
UT code for WoS article
000419821500003
EID of the result in the Scopus database
2-s2.0-85038242375