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
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1129642120
Digital Object Identifier: doi:10.2178/jsl/1129642120
Mathematical Reviews number (MathSciNet):
MR2194242
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
