Infinitely many reducts of homogeneous structures

Bertalan Bodor; Peter Jephson Cameron; Csaba Szabó

doi:10.1007/s00012-018-0526-8

Infinitely many reducts of homogeneous structures

Bertalan Bodor, Peter Jephson Cameron, Csaba Szabó

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

Abstract

This work is dedicated to Tamás E. Schmidt.

It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts.

Original language	English
Article number	43
Number of pages	10
Journal	Algebra Universalis
Volume	79
Early online date	9 May 2018
DOIs	https://doi.org/10.1007/s00012-018-0526-8
Publication status	Published - Jun 2018

Keywords

Homogenous structure
Reduct
Closed subgroup of automosphisms

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10.1007/s00012-018-0526-8

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© 2018 Springer International Publishing AG, part of Springer Nature. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1007/s00012-018-0526-8
Accepted author manuscript, 289 KBLicence: Unspecified

Cite this

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title = "Infinitely many reducts of homogeneous structures",

abstract = "This work is dedicated to Tam{\'a}s E. Schmidt.It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts.",

keywords = "Homogenous structure, Reduct, Closed subgroup of automosphisms",

author = "Bertalan Bodor and Cameron, {Peter Jephson} and Csaba Szab{\'o}",

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AU - Bodor, Bertalan

AU - Cameron, Peter Jephson

AU - Szabó, Csaba

N1 - Funding: National Research, Development and Innovation Fund of Hungary, financed under the FK 124814 funding scheme (second author).

PY - 2018/6

Y1 - 2018/6

N2 - This work is dedicated to Tamás E. Schmidt.It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts.

AB - This work is dedicated to Tamás E. Schmidt.It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts.

KW - Homogenous structure

KW - Reduct

KW - Closed subgroup of automosphisms

U2 - 10.1007/s00012-018-0526-8

DO - 10.1007/s00012-018-0526-8

M3 - Article

SN - 0002-5240

VL - 79

JO - Algebra Universalis

JF - Algebra Universalis

M1 - 43

ER -

Infinitely many reducts of homogeneous structures

Abstract

Keywords

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