Automorphisms and Definability (of Reducts) for Upward Complete Structures

The Svenonius theorem establishes the correspondence between definability of relations in a countable structure and automorphism groups these extensions structure. This may help finding description lattice constituted by all spaces (reducts) original Results on lattices were previously obtained only for ω-categorical structures with finite signature. In our work, we introduce concept an upward complete define completion For structures, Galois closed supergroups group is anti-isomorphism. We describe natural class which have completion, call them discretely homogeneous graphs, present explicit construction their completions. establish general localness property graphs examples completable