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Groups in Simple Theories

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Published online by Cambridge University Press:  31 March 2017

Matthias Baaz
Affiliation:
Technische Universität Wien, Austria
Sy-David Friedman
Affiliation:
Universität Wien, Austria
Jan Krajíček
Affiliation:
Academy of Sciences of the Czech Republic, Prague
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Logic Colloquium '01 , pp. 440 - 467
Publisher: Cambridge University Press
Print publication year: 2005

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References

[1] George M., Bergman and Hendrik W., Lenstra, Jr., Subgroups close to normal subgroups,Journal of Algebra, vol. 127 (1989), pp. 80–97.
[2] Steven, Buechler, Anand, Pillay, and Frank O., Wagner, Supersimple theories,Journal of the American Mathematical Society, vol. 14 (2001), pp. 109–124.
[3] Zoé, Chatzidakis and Ehud, Hrushovski, The model theory of difference fields,Transactions of the American Mathematical Society, vol. 351 (1999), pp. 2997–3071.
[4] Gregory, Cherlin and Ehud, Hrushovski, Permutation groups with few orbits on 5-tuples, and their infinite limits, Preprint, 1995.
[5] Paul, Erdös and R., Rado, A partition calculus in set theory,Bulletin of the American Mathematical Society, vol. 62 (1956), pp. 427–489.
[6] Bradd, Hart, Byunghan, Kim, and Anand, Pillay, Coordinatization and canonical bases in simple theories,The Journal of Symbolic Logic, vol. 65 (2000), pp. 293–309.
[7] Ehud, Hrushovski, Contributions to stable model theory,Ph.D. thesis, University of California at Berkeley, USA, 1986.
[8] Ehud, Hrushovski, Pseudo-finite fields and related structures, Preprint, 1991.
[9] Ehud, Hrushovski and Anand, Pillay, Groups definable in local fields and pseudo-finite fields,Israel Journal ofMathematics, vol. 85 (1994), pp. 203–262.
[10] Ehud, Hrushovski and Anand, Pillay, Definable subgroups of algebraic groups over finite fields,Journal für die Reine und Angewandte Mathematik, vol. 462 (1995), pp. 69–91.
[11] Byunghan, Kim, Recent results on simple first-order theories,Model theory of groups and automorphism groups (David, Evans, editor), LMS Lecture Notes 244, Cambridge University Press, Cambridge, United Kingdom, 1997, pp. 202–212.
[12] Byunghan, Kim, Forking in simple unstable theories,Journal of the London Mathematical Society, vol. 57 (1998), pp. 257–267.
[13] Byunghan, Kim, A note on Lascar strong types in simple theories,The Journal of Symbolic Logic, vol. 63 (1998), pp. 926–936.
[14] Byunghan, Kim and Anand, Pillay, Simple theories,Annals of Pure and Applied Logic, vol. 88 (1997).
[15] Anand Pillay, Definability and definable groups in simple theories,The Journal of Symbolic Logic, vol. 63 (1998), pp. 788–796.
[16] Anand, Pillay, Thomas, Scanlon, and Frank O., Wagner, Supersimple division rings,Mathematical Research Letters, vol. 5 (1998), pp. 473–483.
[17] Bruno P., Poizat, Groupes stables, Nur Al-Mantiq Wal-Ma‘rifah, Villeurbanne, France, 1987.
[18] G., Schlichting, Operationen mit periodischen Stabilisatoren,Archiv der Mathematik, vol. 34 (1980), pp. 97–99.
[19] Saharon, Shelah, Simple unstable theories,Annals of Pure and Applied Logic, vol. 19 (1980), pp. 177–203.
[20] Saharon, Shelah, Toward classifying unstable theories,Annals of Pure and Applied Logic, vol. 80 (1996), pp. 229–255.
[21] Frank O., Wagner, Hyperstable theories,Logic: from foundations to applications (European Logic Colloquium 1993) (Charles, Steinhorn, Wilfrid, Hodges, Martin, Hyland, and John, Truss, editors), Oxford University Press, Oxford, United Kingdom, 1996, pp. 483–514.
[22] Frank O., Wagner, Stable groups, LMS LectureNotes 240, CambridgeUniversity Press, Cambridge, United Kingdom, 1997.
[23] Frank O., Wagner, Simple theories, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
[24] Frank O., Wagner, Hyperdefinable groups in simple theories,Journal of Mathematical Logic, vol. 1 (2001), no. 1, pp. 152–172.

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