| A Generalization of Wilkie's Theorem of the Complement, and an Application to Pfaffian Closure (2007) | |||||||||||||||
Abstract | |||||||||||||||
| Using a modification of Wilkie's recent proof of o-minimality for Pfaffian functions, we give an invariant characterization of o-minimal expansions of IR. We apply this to construct the Pfaffian closure of an arbitrary o-minimal expansion of IR. Dept. of Computer Science, University of Bonn, 53117 Bonn, and the International Computer Science Institute, Berkeley, California. Research supported by DFG Grant KA 673/4-1, and by the ESPRIT BR Grants 7097 and EC-US 030 and by DIMACS. Email: marek@cs.uni-bonn.de y Mathematical Institute, University of Edinburgh, Edinburgh EH9 3JZ. Work partially done while at Mathematical Institute, University of Oxford. Research supported in part by a Senior Research Fellowship of the EPSRC. Email: angus@maths.ed.ac.uk 0 Introduction In this paper we improve the main result of [W96] by weakening the assumption that S is determined by its smooth functions. We assume complete familiarity with [W96]. Wilkie starts with a weak structure S which is o-mini... | |||||||||||||||
Publication details | |||||||||||||||
| |||||||||||||||