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Preprint Number 691

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691. Alfred Dolich, Chris Miller and Charles Steinhorn
Expansions of o-minimal structures by dense independent sets
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Submission date: 20 February 2014.

Abstract:

We study expansions M' of o-minimal structures M on densely ordered groups by collections of mutually independent (over M) dense unary predicates. Positive results include: Every open set (of any arity) definable in M' is definable in M; the structure induced in M' on any one of the new predicates is as simple as possible (in a sense that is made precise); Th(M') eliminates imaginaries and is strongly dependent and axiomatized over Th(M) in the most obvious way. Negative results include that M' does not have definable Skolem functions and is neither atomic nor satisfies the exchange property.

Mathematics Subject Classification: 03C64

Keywords and phrases: o-minimal, densely ordered group, independent predicate, open core, elimination of imaginaries, dependent theory, exchange property, definable Skolem functions, atomic model.

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