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arXiv · 1207.6696

An Algebraic Preservation Theorem for Aleph-Zero Categorical Quantified Constraint Satisfaction

Hubie Chen·Moritz Müller
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Abstract

We prove an algebraic preservation theorem for positive Horn definability in aleph-zero categorical structures. In particular, we define and study a construction which we call the periodic power of a structure, and define a periomorphism of a structure to be a homomorphism from the periodic power of the structure to the structure itself. Our preservation theorem states that, over an aleph-zero categorical structure, a relation is positive Horn definable if and only if it is preserved by all periomorphisms of the structure. We give applications of this theorem, including a new proof of the known complexity classification of quantified constraint satisfaction on equality templates.

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Hubie Chen, Moritz Müller. 2012-07-28. An Algebraic Preservation Theorem for Aleph-Zero Categorical Quantified Constraint Satisfaction. https://doi.org/10.2168/lmcs-9(1:15)2013

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