AN ABSTRACT ELEMENTARY CLASS NONAXIOMATIZABLE IN L-infinity,L-kappa

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00113476" target="_blank" >RIV/00216224:14310/19:00113476 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/an-abstract-elementary-class-nonaxiomatizable-in-linfty-kappa/87EC4FD7FED3B22F244271585EAD99B8" target="_blank" >https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/an-abstract-elementary-class-nonaxiomatizable-in-linfty-kappa/87EC4FD7FED3B22F244271585EAD99B8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/jsl.2019.25" target="_blank" >10.1017/jsl.2019.25</a>

Jazyk výsledku

angličtina

Název v původním jazyce

AN ABSTRACT ELEMENTARY CLASS NONAXIOMATIZABLE IN L-infinity,L-kappa

Popis výsledku v původním jazyce

We show that for any uncountable cardinal lambda, the category of sets of cardinality at least lambda and monomorphisms between them cannot appear as the category of points of a topos, in particular is not the category of models of a L-infinity,L-omega-theory. More generally we show that for any regular cardinal kappa &lt; lambda it is neither the category of kappa-points of a kappa-topos, in particular, nor the category of models of a L-infinity,L-kappa-theory. The proof relies on the construction of a categorified version of the Scott topology, which constitute a left adjoint to the functor sending any topos to its category of points and the computation of this left adjoint evaluated on the category of sets of cardinality at least lambda and monomorphisms between them. The same techniques also apply to a few other categories. At least to the category of vector spaces of with bounded below dimension and the category of algebraic closed fields of fixed characteristic with bounded below transcendence degree.

Název v anglickém jazyce

AN ABSTRACT ELEMENTARY CLASS NONAXIOMATIZABLE IN L-infinity,L-kappa

Popis výsledku anglicky

We show that for any uncountable cardinal lambda, the category of sets of cardinality at least lambda and monomorphisms between them cannot appear as the category of points of a topos, in particular is not the category of models of a L-infinity,L-omega-theory. More generally we show that for any regular cardinal kappa &lt; lambda it is neither the category of kappa-points of a kappa-topos, in particular, nor the category of models of a L-infinity,L-kappa-theory. The proof relies on the construction of a categorified version of the Scott topology, which constitute a left adjoint to the functor sending any topos to its category of points and the computation of this left adjoint evaluated on the category of sets of cardinality at least lambda and monomorphisms between them. The same techniques also apply to a few other categories. At least to the category of vector spaces of with bounded below dimension and the category of algebraic closed fields of fixed characteristic with bounded below transcendence degree.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF16_027%2F0008360" target="_blank" >EF16_027/0008360: Postdoc@MUNI</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Journal of Symbolic Logic

ISSN

0022-4812

e-ISSN

—

Svazek periodika

84

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

12

Strana od-do

1240-1251

Kód UT WoS článku

000487036000018

EID výsledku v databázi Scopus

2-s2.0-85072311928