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VOLUME 3, ISSUE 1, PAPER 2
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Cores of Countably Categorical Structures
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Abstract
A relational structure is a core, if all its endomorphisms are embeddings.
This notion is important for computational complexity classification of
constraint satisfaction problems. It is a fundamental fact that every finite
structure has a core, i.e., has an endomorphism such that the structure
induced by its image is a core; moreover, the core is unique up to isomorphism. Weprove that every ω-categorical structure has a core. Moreover, every
ω-categorical structure is homomorphically equivalent to a model-complete
core, which is unique up to isomorphism, and which is finite or
ω-categorical. We discuss consequences for constraint satisfaction with
ω-categorical templates.
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Publication date: January 25, 2007
Full Text: PDF | PostScript
DOI: 10.2168/LMCS-3(1:2)2007
Hit Counts: 1454 |
 Creative Commons | |
