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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GJ18-13685Y" target="_blank" >GJ18-13685Y: Teorie modelů a extrémální kombinatorika</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Transactions of the American Mathematical Society

ISSN

0002-9947

e-ISSN

—

Svazek periodika

375

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

67

Strana od-do

7601-7667

Kód UT WoS článku

000830695900001

EID výsledku v databázi Scopus

2-s2.0-85139565443