Geodesic
Generic Automorphisms
Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 75-97.

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We study generic sequences of automorphisms. For some classes of models (for example, saturated models), we show that every sequence of automorphisms whose length does not exceed the cardinality of the model is the element-wise product of two generic sequences. We also prove that the fixed field of a finite generic sequence of automorphisms of a separably closed field is regularly closed. 
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K. Zh. Kudaibergenov. Generic Automorphisms. Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 75-97. https://geodesic-test.mathdoc.fr/item/MT_2003_6_1_a3/

[1] Ershov Yu. L., “Polya s razreshimoi teoriei”, Dokl. AN SSSR, 174:1 (1967), 19–20 | MR | Zbl

[2] Ershov Yu. L., “Algoritmicheskie problemy v teorii polei”, Spravochnaya kniga po matematicheskoi logike, Chast III: Dopolnenie, Nauka, M., 1982, 269–353

[3] Iekh T., Teoriya mnozhestv i metod forsinga, Mir, M., 1973

[4] Kudaibergenov K. Zh., “O nepodvizhnom pole genericheskogo avtomorfizma”, Mat. trudy, 4:1 (2001), 25–35 | MR

[5] Kudaibergenov K. Zh., “Odnorodnye modeli i stabilnye diagrammy”, Sib. mat. zhurn., 43:5 (2002), 1064–1076 | MR | Zbl

[6] Chatzidakis Z., “Generic automorphisms of separably closed fields”, Illinois J. Math., 45:3 (2001), 693–733 | MR | Zbl

[7] Chatzidakis Z., Hrushovski E., “Model theory of difference fields”, Trans. Amer. Math. Soc., 351 (1999), 2997–3071 | DOI | MR | Zbl

[8] Hodges W., Hodkinson I., Lascar D., Shelah S., “The small index property for $\omega$-stable $\omega$-categorical structures and for the random graph”, J. London Math. Soc. (2), 48:2 (1993), 204–218 | DOI | MR | Zbl

[9] Keisler H. J., Morley M. D., “On the number of homogeneous models of a given power”, Israel J. Math., 5:2 (1967), 73–78 | DOI | MR | Zbl

[10] Kudaibergenov K. Zh., “Homogeneous models of stable theories”, Siberian Adv. Math., 3:3 (1993), 56–88 | MR

[11] Lascar D., “Autour de la propriété du petit indice (On the small index property)”, Proc. London. Math. Soc. (3), 62:1 (1991), 25–53 | DOI | MR | Zbl

[12] Lascar D., “Les beaux automorphismes (The beautiful automorphisms)”, Arch. Math. Logic, 31:1 (1991), 55–68 | DOI | MR | Zbl

[13] Lascar D., Shelah S., “Uncountable saturated structures have the small index property”, Bull. London. Math. Soc., 25:2 (1993), 125–131 | DOI | MR | Zbl

[14] Macintyre A., “Generic automorphisms of fields”, Ann. Pure Appl. Logic, 88:2–3 (1997), 165–180 | DOI | MR | Zbl

[15] Shelah S., “Finite diagrams stable in power”, Ann. Math. Logic, 2:1 (1970), 69–118 | DOI | MR | Zbl

[16] Shelah S., “The lazy model-theoretician's guide to stability”, Logique et Analyse, 18:71–72 (1975), 241–308 | MR | Zbl

[17] Shelah S., Classification Theory and the Number of Nonisomorphic Models, North-Holland, Amsterdam, 1978 | MR | Zbl

[18] Truss J., “Generic automorphisms of homogeneous structures”, Proc. London Math. Soc. (3), 65:1 (1992), 121–141 | DOI | MR | Zbl

[19] Wood C., “Notes on the stability of separably closed fields”, J. Symbolic Logic, 44:3 (1979), 412–416 | DOI | MR | Zbl