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An analogue of the Baire category theorem

Published online by Cambridge University Press:  12 March 2014

Philipp Hieronymi
Philipp Hieronymi*
Affiliation:
University of Illinois at Urbana-Champaign, Department of Mathematics, 1409 W. Green Street, Urbana, IL 61801, USA, E-mail: P@hieronymi.de
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Abstract

Every definably complete expansion of an ordered field satisfies an analogue of the Baire Category Theorem.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 207 - 213
Copyright
Copyright © Association for Symbolic Logic 2013

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References

REFERENCES

[1]Dolich, A., Miller, C., and Steinhorn, C., Structures having o-minimal open core, Transactions of the American Mathematical Society, vol. 362 (2010), no. 3, pp. 1371–1411.CrossRefGoogle Scholar
[2]Fornasiero, A., Definably complete structures are not pseudo-enumerable, Archive for Mathematical Logic, vol. 50 (2011), no. 5-6, pp. 603–615.CrossRefGoogle Scholar
[3]Fornasiero, A. and Servi, T., Definably complete Baire structures, Fundamenta Mathematicae, vol. 209 (2010), no. 3, pp. 215–241.CrossRefGoogle Scholar
[4]Fornasiero, A. and Servi, T., Theorems of the complement. Lecture notes on O-minimal structures and real analytic geometry (Miller, C., Rolin, J.-P., and Speissegger, P., editors), Fields Institute Communications, vol. 62, Springer, 2012, pp. 219–242.CrossRefGoogle Scholar
[5]Fornasiero, A. and Servi, T., Pfaffian closure for definably complete Baire structures, Illinois Journal of Mathematics, to appear.Google Scholar
[6]Hieronymi, P., Defining the set of integers in expansions of the real field by a closed discrete set, Proceedings of the American Mathematical Society, vol. 138 (2010), no. 6, pp. 2163–2168.CrossRefGoogle Scholar
[7]Miller, C., Expansions of dense linear orders with the intermediate value property, this Journal, vol. 66 (2001), no. 4, pp. 1783–1790.Google Scholar