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Title: | Endolocality meets homomorphism-homogeneity: a new approach in the study of relational algebras | Authors: | Pech Maja | Keywords: | endolocality – endomorphism monoid – weak Krasner algebra – relational clone – relational algebra – quantifier elimination – homomorphism-homogeneity – Galois connection – relational structure – weak Krasner clone – weakly oligomorphic | Issue Date: | 2011 | Journal: | Algebra Universalis | Abstract: | We study the problem of characterizing all relations that can be defined from the fundamental relations of a given relational structure using positive existential formulæ. The notion of κ-endolocality is introduced in order to measure the complexity of relational structures with respect to this task. The hierarchy of κ-endolocal structures is thoroughly analysed in algebraic and model-theoretic ways. Interesting cross-connections with homomorphism-homogeneous relational structures are revealed. The interrelations between endolocal relational structures and several model-theoretic notions are collected in the Main Theorem. This Main Theorem is demonstrated to be a useful tool for studying relational algebras and, in particular, weak Krasner algebras. For example, a short proof of F. Börners characterization of weak Krasner clones on a countable set is given. | URI: | https://open.uns.ac.rs/handle/123456789/24574 | ISSN: | 0002-5240 1420-8911 |
Appears in Collections: | PMF Publikacije/Publications |
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