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Topological Model Theory by Jörg Flum , Martin Ziegler
English | PDF | 1980 | 161 Pages | ISBN : 3540097325 | 5.9 MB
The task of model theory is to investigate mathematical structures with the aid of formal languages. Classical model theory deals with algebraic struc- tures. Topological model theory investigates topological structures. A to- pological structure is a pair (=,a) consisting of an algebraic structure ~ and a topology ~ on A. Topological groups and topological vector spaces are examples. The formal language in the study of topological structures is L t- This is the fragment of the (monadic) second-order language (the set variab- les ranging over the topology ~) obtained by allowing quantification over set variables in the form 3X(t e X ^ ~), wheret is a term and the second- order variable X occurs only negatively in ~ (and dually for the universal quantifier). Intuitively, L t allows only quantifications over sufficiently small neighborhoods of a point.

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