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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
What would the rational Urysohn space and the random graph look like if they were uncountable?
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX20-31529X" target="_blank" >GX20-31529X: Abstract convergence schemes and their complexities</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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