2 ℵ No pairwise non-isomorphic maximal-closed subgroups of Sym(N) via the classification of the reducts of the Henson digraphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384109" target="_blank" >RIV/00216208:11320/18:10384109 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1017/jsl.2017.74" target="_blank" >https://doi.org/10.1017/jsl.2017.74</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/jsl.2017.74" target="_blank" >10.1017/jsl.2017.74</a>

Jazyk výsledku

angličtina

Název v původním jazyce

2 ℵ No pairwise non-isomorphic maximal-closed subgroups of Sym(N) via the classification of the reducts of the Henson digraphs

Popis výsledku v původním jazyce

Given two structures M and N on the same domain, we say that N is a reduct of M if all EMPTY SET -definable relations of N are EMPTY SET -definable in M . In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are ℵ 0 -categorical, determining their reducts is equivalent to determining all closed supergroups G&lt; Sym(N) of their automorphism groups. A consequence of the classification is that there are 2 ℵ 0 pairwise non-isomorphic Henson digraphs which have no proper non-trivial reducts. Taking their automorphisms groups gives a positive answer to a question of Macpherson that asked if there are 2 ℵ 0 pairwise non-conjugate maximal-closed subgroups of Sym(N) . By the reconstruction results of Rubin, these groups are also non-isomorphic as abstract groups.

Název v anglickém jazyce

2 ℵ No pairwise non-isomorphic maximal-closed subgroups of Sym(N) via the classification of the reducts of the Henson digraphs

Popis výsledku anglicky

Given two structures M and N on the same domain, we say that N is a reduct of M if all EMPTY SET -definable relations of N are EMPTY SET -definable in M . In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are ℵ 0 -categorical, determining their reducts is equivalent to determining all closed supergroups G&lt; Sym(N) of their automorphism groups. A consequence of the classification is that there are 2 ℵ 0 pairwise non-isomorphic Henson digraphs which have no proper non-trivial reducts. Taking their automorphisms groups gives a positive answer to a question of Macpherson that asked if there are 2 ℵ 0 pairwise non-conjugate maximal-closed subgroups of Sym(N) . By the reconstruction results of Rubin, these groups are also non-isomorphic as abstract groups.

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

2018

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

2018

Číslo periodika v rámci svazku

83

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

395-415

Kód UT WoS článku

000440465700001

EID výsledku v databázi Scopus

2-s2.0-85051012055