Local methods for relational structures and their weak Krasneralgebras

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.