What would the rational Urysohn space and the random graph look like if they were uncountable?

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00619400" target="_blank" >RIV/67985840:_____/25:00619400 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00153-024-00948-z" target="_blank" >https://doi.org/10.1007/s00153-024-00948-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00153-024-00948-z" target="_blank" >10.1007/s00153-024-00948-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

What would the rational Urysohn space and the random graph look like if they were uncountable?

Popis výsledku v původním jazyce

Building on the work of Avraham, Rubin, and Shelah, we aim to build a variant of the Fraïssé theory for uncountable models built from finite submodels. With this aim, we generalize the notion of an increasing set of reals to other structures. As an application, we prove that the following is consistent: there exists an uncountable, separable metric space X with rational distances, such that every uncountable partial 1-1 function from X to X is an isometry on an uncountable subset. We aim for a general theory of structures with this kind of properties. This includes results about the automorphism groups, and partial classification results.

Název v anglickém jazyce

What would the rational Urysohn space and the random graph look like if they were uncountable?

Popis výsledku anglicky

Building on the work of Avraham, Rubin, and Shelah, we aim to build a variant of the Fraïssé theory for uncountable models built from finite submodels. With this aim, we generalize the notion of an increasing set of reals to other structures. As an application, we prove that the following is consistent: there exists an uncountable, separable metric space X with rational distances, such that every uncountable partial 1-1 function from X to X is an isometry on an uncountable subset. We aim for a general theory of structures with this kind of properties. This includes results about the automorphism groups, and partial classification results.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX20-31529X" target="_blank" >GX20-31529X: Abstraktní konvergenční schémata a jejich složitost</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Archive for Mathematical Logic

ISSN

0933-5846

e-ISSN

1432-0665

Svazek periodika

64

Číslo periodika v rámci svazku

3-4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

28

Strana od-do

445-472

Kód UT WoS článku

001344740000001

EID výsledku v databázi Scopus

2-s2.0-105003766289