| o-Minimal Expansions of the Real Field: A Characterization, and an Application to Pfaffian Closure (1997) | |||||||||||||||
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| Using a modification of Wilkie's recent proof of o-minimality for Pfaffian functions, we gave 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 Oxford, Oxford OX1 3LB. Research supported in part by a Senior Research Fellowship of the SERC. Email: ajm@maths.ox.ac.uk 0 Introduction While working on complexity questions for V C-dimension of general neural networks and corresponding semi-Pfaffian sets [KM97a], we became convinced that major progress on o-minimality should come from a more systematic use of Sard's Theorem and Morse Theory [H76]. The importance of these for Khovanski'... | |||||||||||||||
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