A wild model of linear arithmetic and discretely ordered modules

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/61384399:31140/17:00051531

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

A wild model of linear arithmetic and discretely ordered modules

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

A wild model of linear arithmetic and discretely ordered modules

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematical Logic Quarterly

ISSN

0942-5616

e-ISSN

—

Svazek periodika

63

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

8

Strana od-do

501-508

Kód UT WoS článku

000419821500003

EID výsledku v databázi Scopus

2-s2.0-85038242375