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PROJECTIVE CLONE HOMOMORPHISMS

Part of: Algebraic structures Model theory

Published online by Cambridge University Press:  03 May 2019

MANUEL BODIRSKY ,
MICHAEL PINSKER  and
ANDRÁS PONGRÁCZ
MANUEL BODIRSKY
Affiliation:
INSTITUT FÜR ALGEBRA TECHNISCHE UNIVERSITÄT DRESDEN 01062 DRESDEN, GERMANY E-mail: Manuel.Bodirsky@tu-dresden.de URL: http://www.math.tu-dresden.de/~bodirsky/
MICHAEL PINSKER
Affiliation:
INSTITUT FÜR DISKRETE MATHEMATIK UND GEOMETRIE FG ALGEBRA, TECHNISCHE UNIVERSITÄT WIEN WIEN, AUSTRIA and DEPARTMENT OF ALGEBRA CHARLES UNIVERSITY PRAGUE, CZECH REPUBLIC E-mail: marula@gmx.at  URL: http://dmg.tuwien.ac.at/pinsker/
ANDRÁS PONGRÁCZ
Affiliation:
DEPARTMENT OF ALGEBRA AND NUMBER THEORY UNIVERSITY OF DEBRECEN 4032 DEBRECEN, EGYETEM SQUARE 1, HUNGARY E-mail: pongracz.andras@science.unideb.hu
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Abstract

It is known that a countable $\omega $-categorical structure interprets all finite structures primitively positively if and only if its polymorphism clone maps to the clone of projections on a two-element set via a continuous clone homomorphism. We investigate the relationship between the existence of a clone homomorphism to the projection clone, and the existence of such a homomorphism which is continuous and thus meets the above criterion.

Keywords

clonehomogeneous structureautomatic continuitytrivial algebrapolymorphism cloneconstraint satisfaction problemcanonical function

MSC classification

Primary: 03C05: Equational classes, universal algebra
Secondary: 03C40: Interpolation, preservation, definability 08A70: Applications of universal algebra in computer science 08A35: Automorphisms, endomorphisms 08A30: Subalgebras, congruence relations

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 1 , March 2021 , pp. 148 - 161
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Copyright
© The Association for Symbolic Logic 2019

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References

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