Universal Structures

Details Universal Structures Universal Structures

2004-05-10

arxiv.org/abs/math/0405159v2

Mathematics

Logic

Scientific paper

We deal with the existence of universal members in a cardinality class of abelian groups, specifically with the existence of universal members in cardinalities which are strong limit singular of countable cofinality. We then deal with the oak property (from a work of Dzamonja and the author), a property of complete first order theories, sufficient for the non-existence of universal models under suitable cardinal assumptions. We prove that it holds for the class of groups (naturally interpreted) and deal more with the existence of universals.

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