Elimination of imaginaries in expansions of o-minimal structures by generic sets
Sergio Fratarcangeli
Source: J. Symbolic Logic Volume 70, Issue 4 (2005), 1150-1160.
Abstract
Let TP be the theory obtained by adding a generic predicate to an o-minimal theory T. We prove that if T admits elimination of imaginaries, then TP also admits elimination of imaginaries.
Primary Subjects: 03C64
Keywords: generic predicates; elimination of imaginaries; o-minimal structures
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1129642120
Digital Object Identifier: doi:10.2178/jsl/1129642120
References
Z. Chatzidakis and A. Pillay Generic structures and simple theories, Annals of Pure and Applied Logic ,(1998), no. 95, pp. 71--92.
Mathematical Reviews (MathSciNet):
MR1650667
Digital Object Identifier: doi:10.1016/S0168-0072(98)00021-9
H. Friedman On expansions of o-minimal structures, www.math.ohio-state.edu/$\sim$friedman} ,{1996.
D. Haskell, E. Hrushovski, and D. Macpherson Definable sets in algebraically closed valued fields, Part I: Elimination of imaginaries, preprint, pp. 44--45 ,2002.
W. Hodges Model theory, Cambridge University Press ,1993.
Mathematical Reviews (MathSciNet):
MR1221741
Zentralblatt MATH:
0789.03031
C. Miller Tameness in expansions of the real field, Logic Colloquium '01 (Vienna), Lecture Notes in Logic, vol. 20, Association of Symbolic Logic ,2005, pp. 281--316.
C. Miller and P. Speissegger Expansions of the real line by open sets: o-minimality and open cores, Fundamenta Mathematicae ,(1999), no. 162, pp. 193--208.
Mathematical Reviews (MathSciNet):
MR1736360
C. Miller and C. Steinhorn Expansions of densely ordered groups: o-minimality and open cores, preprint.
B. Poizat A course in model theory, Springer-Verlag ,2000.
Mathematical Reviews (MathSciNet):
MR1757487
Zentralblatt MATH:
0951.03002
L. van den Dries Tame topology and o-minimal structures, Cambridge University Press ,1998.
Mathematical Reviews (MathSciNet):
MR1633348
Zentralblatt MATH:
0953.03045
M. Ziegler Introduction to stability theory and Morley rank, Model theory and algebraic geometry An introduction to E. Hrushovski's proof of the Geometric Mordell-Lang Conjecture (E. Bouscaren, editor), Springer-Verlag ,1998, pp. 19--44.
Mathematical Reviews (MathSciNet):
MR1678594
Zentralblatt MATH:
0925.03163