Geodesic
On the independence property of first order theories and indiscernible sequences
Matematičeskie trudy, Tome 14 (2011) no. 1, pp. 126-140 
K. Zh. Kudaibergenov. On the independence property of first order theories and indiscernible sequences. Matematičeskie trudy, Tome 14 (2011) no. 1, pp. 126-140. http://geodesic.mathdoc.fr/item/MT_2011_14_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We refute the strong version of Shelah's conjecture about models of large cardinalities, the independence property, and indiscernible sequences. We find necessary and sufficient conditions for a theory to lack the independence property and present applications of these conditions.

[1] Ershov Yu. L., Palyutin E. A., Matematicheskaya logika, Nauka, M., 1987 | MR | Zbl

[2] Kudaibergenov K. Zh., “Slabo kvazi-minimalnye modeli”, Matem. tr., 13:1 (2010), 156–168 | MR

[3] Belegradek O., Peterzil Y., Wagner F., “Quasi-minimal structures”, J. Symbolic Logic, 65:3 (2000), 1115–1132 | DOI | MR | Zbl

[4] Macpherson D., Marker D., Steinhorn C., “Weakly o-minimal structures and real closed fields”, Trans. Amer. Math. Soc., 352:12 (2000), 5435–5483 | DOI | MR | Zbl

[5] Parigot M., “Théories d'arbres”, J. Symbolic Logic, 47:4 (1982), 841–853 | DOI | MR | Zbl

[6] Pillay A., Steinhorn C., “Definable sets in ordered structures. I”, Trans. Amer. Math. Soc., 295:2 (1986), 565–592 | DOI | MR | Zbl

[7] Poizat B., “Théories instables”, J. Symbolic Logic, 46:3 (1981), 513–522 | DOI | MR | Zbl

[8] Shelah S., Classification Theory and the Number of Nonisomorphic Models, Studies in Logic and the Foundations of Mathematics, 92, North-Holland Publishing Co., Amsterdam–New York, 1978 | MR | Zbl

[9] Shelah S., Around Classification Theory of Models, Lecture Notes in Math., 1182, Springer, Berlin, 1986 | Zbl