The independence property in generalized dense pairs of structures
Alexander Berenstein, Alf Dolich, and Alf Onshuus
Source: J. Symbolic Logic Volume 76, Issue 2
(2011), 391-404.
Abstract
We provide a general theorem implying that for a (strongly) dependent theory T the theory of sufficiently well-behaved pairs of models of T is again (strongly) dependent. We apply the theorem to the case of lovely pairs of thorn-rank one theories as well as to a setting of dense pairs of first-order topological theories.
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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1305810754
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Zentralblatt MATH identifier: 05913841
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References
H. Adler, A geometric introduction to forking and thorn-forking, preprint, available at www.amsta.leeds.ac.uk/~adler.
Mathematical Reviews (MathSciNet): MR2665779
Zentralblatt MATH: 05774857
Digital Object Identifier: doi:10.1142/S0219061309000811
B. Baizhanov and J. Baldwin, Local homogeneity, Journal of Symbolic Logic, vol. 69 (2004), pp. 1243–1260.
Mathematical Reviews (MathSciNet): MR2135665
Zentralblatt MATH: 1071.03019
Digital Object Identifier: doi:10.2178/jsl/1102022221
Project Euclid: euclid.jsl/1102022221
I. Ben Yaacov, A. Pillay, and E. Vassiliev, Lovely pairs of models, Annals of Pure and Applied Logic, vol. 122 (2003), pp. 235–261.
Mathematical Reviews (MathSciNet): MR1992524
Zentralblatt MATH: 1030.03026
Digital Object Identifier: doi:10.1016/S0168-0072(03)00018-6
A. Berenstein and E. Vassiliev, On lovely pairs of geometric structures, Annals of Pure and Applied Logic, vol. 161 (2010), pp. 866–878.
Mathematical Reviews (MathSciNet): MR2601016
Digital Object Identifier: doi:10.1016/j.apal.2009.10.004
G. Boxall, NIP for some pair-like theories, Modnet preprint #181.
S. Buechler, Pseudoprojective strongly minimal sets are locally projective, Journal of Symbolic Logic, vol. 56 (1991), pp. 1184–1194.
Mathematical Reviews (MathSciNet): MR1136449
Zentralblatt MATH: 0737.03009
Digital Object Identifier: doi:10.2307/2275467
JSTOR: links.jstor.org
E. Casanovas and M. Ziegler, Stable theories with a new predicate, Journal of Symbolic Logic, vol. 66 (2001), pp. 1127–1140.
Mathematical Reviews (MathSciNet): MR1856732
Zentralblatt MATH: 1002.03023
Digital Object Identifier: doi:10.2307/2695097
JSTOR: links.jstor.org
C.C. Chang and H.J. Keisler, Model theory, third ed., Studies in Logic and Foundations of Mathematics, North Holland, 1990.
Mathematical Reviews (MathSciNet): MR1059055
Z. Chatzidakis and A. Pillay, Generic structures and simple theories, Annals of Pure and Applied Logic, (1998), pp. 71–92.
Mathematical Reviews (MathSciNet): MR1650667
Zentralblatt MATH: 0929.03043
Digital Object Identifier: doi:10.1016/S0168-0072(98)00021-9
J. Denef and L. van den Dries, P-adic and real subanalytic sets, The Annals of Mathematics, vol. 128 (1988), pp. 79–138.
Mathematical Reviews (MathSciNet): MR951508
Digital Object Identifier: doi:10.2307/1971463
JSTOR: links.jstor.org
A. Dolich and D. Lippel J. Goodrick, Dp-minimality: basic facts and examples, Modnet preprint #207.
A. Dolich, C. Miller, and C. Steinhorn, Structures having o-minimal open core, Transactions of the American Mathematical Society, vol. 362 (2010), pp. 1371–1411.
Mathematical Reviews (MathSciNet): MR2563733
Zentralblatt MATH: 1197.03042
Digital Object Identifier: doi:10.1090/S0002-9947-09-04908-3
L. van den Dries, Dense pairs of o-minimal structures, Fundamenta Mathematicae, vol. 157 (1998), pp. 61–78.
Mathematical Reviews (MathSciNet): MR1623615
Zentralblatt MATH: 0906.03036
––––, Tame topology and o-minimal structures, London Mathematical Society Lecture Notes Series, vol. 248, Cambridge University Press, Cambridge, 1998.
L. van den Dries and A. Lewenberg, T-convexity and tame extensions, Journal of Symbolic Logic, vol. 60 (1995), pp. 74–102.
Mathematical Reviews (MathSciNet): MR1324502
Digital Object Identifier: doi:10.2307/2275510
JSTOR: links.jstor.org
A. Günaydin and P. Hieronymi, Dependent pairs, to be published in this Journal.
D. Haskell and D. Macpherson, A version of o-minimality for the p-adics, Journal of Symbolic Logic, vol. 62 (1997), pp. 1075–1092.
Mathematical Reviews (MathSciNet): MR1618009
Zentralblatt MATH: 0894.03015
Digital Object Identifier: doi:10.2307/2275628
JSTOR: links.jstor.org
D. Macpherson, D. Marker, and C. Steinhorn, Weakly o-minimal structures and real closed fields, Transactions of the American Mathematical Society, vol. 352 (2000), pp. 5435–5483.
Mathematical Reviews (MathSciNet): MR1781273
Zentralblatt MATH: 0982.03021
Digital Object Identifier: doi:10.1090/S0002-9947-00-02633-7
JSTOR: links.jstor.org
L. Matthews, Cell decomposition and dimension functions in first-order topological structures, Proceedings of the London Mathematical Society, vol. s3-70 (1995), pp. 1–32.
Mathematical Reviews (MathSciNet): MR1300839
Zentralblatt MATH: 0829.03019
Digital Object Identifier: doi:10.1112/plms/s3-70.1.1
A. Onshuus, Properties and consequences of thorn-independence, Journal of Symbolic Logic, vol. 71 (2006), pp. 1–21.
Mathematical Reviews (MathSciNet): MR2210053
Zentralblatt MATH: 1103.03036
Digital Object Identifier: doi:10.2178/jsl/1140641160
Project Euclid: euclid.jsl/1140641160
A. Pillay, On externally definable sets and a theorem of Shelah, preprint, available at www.amsta.leeds.ac.uk/~pillay/.
Mathematical Reviews (MathSciNet): MR2412902
Zentralblatt MATH: 1135.03337
B. Poizat, Paires de structures stables, Journal of Symbolic Logic, vol. 48 (1983), pp. 239–249.
Mathematical Reviews (MathSciNet): MR704080
Zentralblatt MATH: 0525.03023
Digital Object Identifier: doi:10.2307/2273543
JSTOR: links.jstor.org
S. Shelah, Strongly dependent theories, SH863, available at shelah.logic.at/.
––––, Dependent first order theories, continued, Israel Journal of Mathematics, vol. 173(2009), no. 1, pp. 1–60.
E. Vassiliev, Generic pairs of SU-rank 1 structures, Annals of Pure and Applied Logic, vol. 120 (2003), pp. 103–149.
Mathematical Reviews (MathSciNet): MR1949704
Zentralblatt MATH: 1010.03023
Digital Object Identifier: doi:10.1016/S0168-0072(02)00060-X
