Automorphisms and strongly invariant relations

Ferdinand Börner; Martin Goldstern; Saharon Shelah

doi:10.1007/s00012-023-00818-4

Automorphisms and strongly invariant relations

Ferdinand Börner
, Martin Goldstern^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate characterizations of the Galois connection Aut - sInv between sets of finitary relations on a base set A and their automorphisms. In particular, for A= ω₁ , we construct a countable set R of relations that is closed under all invariant operations on relations and under arbitrary intersections, but is not closed under sInv Aut . Our structure (A, R) has an ω -categorical first order theory. A higher order definable well-order makes it rigid, but any reduct to a finite language is homogeneous.

Original language	English
Article number	27
Journal	Algebra Universalis
Volume	84
Issue number	4
DOIs	https://doi.org/10.1007/s00012-023-00818-4
State	Published - Nov 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).

Keywords

Galois closure
Homogeneous reduct
Invariant operations
Krasner algebra
Rigid algebra

Access to Document

10.1007/s00012-023-00818-4

Cite this

@article{e33d3059b1a74e5bbbc6aa7878b5cce6,

title = "Automorphisms and strongly invariant relations",

abstract = "We investigate characterizations of the Galois connection Aut - sInv between sets of finitary relations on a base set A and their automorphisms. In particular, for A= ω1 , we construct a countable set R of relations that is closed under all invariant operations on relations and under arbitrary intersections, but is not closed under sInv Aut . Our structure (A, R) has an ω -categorical first order theory. A higher order definable well-order makes it rigid, but any reduct to a finite language is homogeneous.",

keywords = "Galois closure, Homogeneous reduct, Invariant operations, Krasner algebra, Rigid algebra",

author = "Ferdinand B{\"o}rner and Martin Goldstern and Saharon Shelah",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s).",

year = "2023",

month = nov,

doi = "10.1007/s00012-023-00818-4",

language = "אנגלית",

volume = "84",

journal = "Algebra Universalis",

issn = "0002-5240",

publisher = "Springer International Publishing",

number = "4",

}

TY - JOUR

T1 - Automorphisms and strongly invariant relations

AU - Börner, Ferdinand

AU - Goldstern, Martin

AU - Shelah, Saharon

PY - 2023/11

Y1 - 2023/11

N2 - We investigate characterizations of the Galois connection Aut - sInv between sets of finitary relations on a base set A and their automorphisms. In particular, for A= ω1 , we construct a countable set R of relations that is closed under all invariant operations on relations and under arbitrary intersections, but is not closed under sInv Aut . Our structure (A, R) has an ω -categorical first order theory. A higher order definable well-order makes it rigid, but any reduct to a finite language is homogeneous.

AB - We investigate characterizations of the Galois connection Aut - sInv between sets of finitary relations on a base set A and their automorphisms. In particular, for A= ω1 , we construct a countable set R of relations that is closed under all invariant operations on relations and under arbitrary intersections, but is not closed under sInv Aut . Our structure (A, R) has an ω -categorical first order theory. A higher order definable well-order makes it rigid, but any reduct to a finite language is homogeneous.

KW - Galois closure

KW - Homogeneous reduct

KW - Invariant operations

KW - Krasner algebra

KW - Rigid algebra

UR - https://www.scopus.com/pages/publications/85168299387

U2 - 10.1007/s00012-023-00818-4

DO - 10.1007/s00012-023-00818-4

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85168299387

SN - 0002-5240

VL - 84

JO - Algebra Universalis

JF - Algebra Universalis

IS - 4

M1 - 27

ER -

Automorphisms and strongly invariant relations

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this