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PROJECTIVE CLONE HOMOMORPHISMS

Published online by Cambridge University Press:  03 May 2019

MANUEL BODIRSKY
Affiliation:
INSTITUT FÜR ALGEBRA TECHNISCHE UNIVERSITÄT DRESDEN01062DRESDEN, GERMANY E-mail:Manuel.Bodirsky@tu-dresden.deURL: http://www.math.tu-dresden.de/~bodirsky/
MICHAEL PINSKER
Affiliation:
INSTITUT FÜR DISKRETE MATHEMATIK UND GEOMETRIE FG ALGEBRA, TECHNISCHE UNIVERSITÄT WIENWIEN, 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 DEBRECEN4032DEBRECEN, EGYETEM SQUARE 1, HUNGARY E-mail:pongracz.andras@science.unideb.hu

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.

Type
Article
Copyright
© The Association for Symbolic Logic 2019

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