Local methods for relational structures and their weak Krasneralgebras

Pech, Maja

Lokalnemetode za relacione strukture i njihove slabe Krasnerove algebre

Abstract

In this thesis local methods are made available as a tool to study the unary parts of clones (or, equivalently, the weak Krasner algebras). Using the language of model theory and Galois connections we develop a link between homomorphism-homogeneous relational structures and local methods, via the notion of endolocality. The theoretical results that are obtained are used to develop a systematic theory for the classification of homomorphism-homogeneous relational structures.

U ovoj tezi su razvijene lokalne metode koje se mogu koristiti za izu- ˇcavanje unarnih delova klonova (ili, ekvivalentno, slabih Krasnerovih algebri). Koriˇs´cenjem jezika teorije modela i Galoovih veza uspostavljen je odnos izmedu homomorfizam-homogenih relacionih struktura i lokalnih metoda, preko pojma endolokalnosti. Dobijeni teoretski rezultati su upotrebljeni za razvoj sistematske teorije za klasifikaciju homomorfizam-homogenih struktura.

Faculty:
University of Novi Sad, Faculty of Science
Date:
22-05-2009

Keywords:

local methods / lokalne metode / relational structure / clone theory / Galois connections / endomorphismmonoids / weak Krasner algebras / homomorphism-homogeneity / Rosenberg relations / endolocality / one-point extension. / relacione strukture / teorija klonova / veze Galoa / monoidi endomorfizama / slabe Krasnerove algebre / homomorfizam-homogenost / Rozenbergove relacije / endolokalnost / proˇsirenje za jednu taˇcku.

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