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Preprint Number 512

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512. Alfred Dolich, Chris Miller and Charles Steinhorn
Extensions of ordered theories by generic predicates

Submission date: 11 October 2012


Let T be a theory extending that of infinite linear orders. We define what we mean by extensions T' of T by generic unary predicates. Building on work of Chatzidakis and Pillay, we show that such T' exist if and only no model of T defines a unary set having an initial segment isomorphic to (N,<). We then give some results concerning preservation of certain topological properties when passing from T to T'.

Mathematics Subject Classification: 03C64

Keywords and phrases: generic predicate

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