All those EPPA classes (strengthenings of the Herwig-Lascar theorem)

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10454164" target="_blank" >RIV/00216208:11320/22:10454164 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=GTX0QcE~oF" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=GTX0QcE~oF</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/tran/8654" target="_blank" >10.1090/tran/8654</a>

Result language

angličtina

Original language name

All those EPPA classes (strengthenings of the Herwig-Lascar theorem)

Original language description

Let A be a finite structure. We say that a finite structure B is an extension property for partial automorphisms (EPPA)-witness for A if it contains A as a substructure and every isomorphism of substructures of A extends to an automorphism of B. Class C of finite structures has the EPPA (also called the Hrushovski property) if it contains an EPPA-witness for every structure in C. We develop a systematic framework for combinatorial constructions of EPPA-witnesses satisfying additional local properties and thus for proving EPPA for a given class C. Our constructions are elementary, self-contained and lead to a common strengthening of the Herwig-Lascar theorem on EPPA for relational classes defined by forbidden homomorphisms, the Hodkinson-Otto theorem on EPPA for relational free amalgamation classes, its strengthening for unary functions by Evans, Hubička and Nešetřil and their coherent variants by Siniora and Solecki. We also prove an EPPA analogue of the main results of J. Hubička and J. Nešetřil: All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms), thereby establishing a common framework for proving EPPA and the Ramsey property. There are numerous applications of our results, we include a solution of a problem related to a class constructed by the Hrushovski predimension construction. We also characterize free amalgamation classes of finite Γ_L-structures with relations and unary functions which have EPPA.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GJ18-13685Y" target="_blank" >GJ18-13685Y: Model thoery and extremal combinatorics</a><br>

Continuities

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

Publication year

2022

Confidentiality

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

Name of the periodical

Transactions of the American Mathematical Society

ISSN

0002-9947

e-ISSN

—

Volume of the periodical

375

Issue of the periodical within the volume

11

Country of publishing house

US - UNITED STATES

Number of pages

67

Pages from-to

7601-7667

UT code for WoS article

000830695900001

EID of the result in the Scopus database

2-s2.0-85139565443