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ON THE AUTOMORPHISM GROUP OF THE UNIVERSAL HOMOGENEOUS MEET-TREE

Part of: Structure and classification of infinite or finite groups Permutation groups Connections with other structures, applications Model theory Ordered sets Set theory

Published online by Cambridge University Press:  01 February 2021

ITAY KAPLAN ,
TOMASZ RZEPECKI  and
DAOUD SINIORA
ITAY KAPLAN
Affiliation:
EINSTEIN INSTITUTE OF MATHEMATICS HEBREW UNIVERSITY OF JERUSALEM 91904, JERUSALEM, ISRAELE-mail: [email protected]
TOMASZ RZEPECKI
Affiliation:
EINSTEIN INSTITUTE OF MATHEMATICS HEBREW UNIVERSITY OF JERUSALEM 91904, JERUSALEM, ISRAEL and INSTYTUT MATEMATYCZNY UNIWERSYTET WROCŁAWSKI PL. GRUNWALDZKI 2/4 50-384 WROCŁAW, POLANDE-mail: [email protected]
DAOUD SINIORA
Affiliation:
INDEPENDENT SCHOLAR E-mail: [email protected]
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Abstract

We show that the countable universal homogeneous meet-tree has a generic automorphism, but it does not have a generic pair of automorphisms.

Keywords

Fraïssé limitgeneric automorphismtreePolish groupample generics

MSC classification

Primary: 03C15: Denumerable structures
Secondary: 03E15: Descriptive set theory 06A12: Semilattices 20E08: Groups acting on trees 54H11: Topological groups 20B27: Infinite automorphism groups
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 4 , December 2021 , pp. 1508 - 1540
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Copyright
© Association for Symbolic Logic 2021

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