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Characterizing rosy theories

Published online by Cambridge University Press:  12 March 2014

Clifton Ealy  and
Alf Onshuus
Clifton Ealy
Affiliation:
University of Illinois at Urbana-Champaign, Department of Mathematics, 1409 West Green Street, Urbana, Illinois 61801, USA, E-mail: clif@math.uiuc.edu
Alf Onshuus
Affiliation:
Universidad de Los Andes, Departemento de Matemáticas CRA. 1 NO 18A-10 Bogotá, Colombia, E-mail: onshuus@gmail.com
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Abstract

We examine several conditions, either the existence of a rank or a particular property of þ-forking that suggest the existence of a well-behaved independence relation, and determine the consequences of each of these conditions towards the rosiness of the theory. In particular we show that the existence of an ordinal valued equivalence relation rank is a (necessary and) sufficient condition for rosiness.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 3 , September 2007 , pp. 919 - 940
Copyright
Copyright © Association for Symbolic Logic 2007

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References

REFERENCES

[CH04]Chatzidakis, Zoé and Hrushovski, Ehud, Perfect pseudo-algebraically closedfields are algebraically bounded, Journal of Algebra, vol. 271 (2004), no. 2, pp. 627–637.CrossRefGoogle Scholar
[Eal04]Ealy, Clifton, Thorn forking in simple theories and a Manin-Mumford theorem for T-modules, Ph.D. thesis, University of California at Berkeley, 2004.Google Scholar
[Gag05]Gagelman, Jerry, Stability in geometric theories, Annals of Pure and Applied Logic, vol. 132 (2005), no. 2-3, pp. 313–326.CrossRefGoogle Scholar
[HKP00]Hart, Bradd, Kim, Byunghan, and Pillay, Anand, Coordinatisation and canonical bases in simple theories, this Journal, vol. 65 (2000), no. 1, pp. 293–309.Google Scholar
[HP94]Hrushovski, Ehud and Pillay, Anand, Groups definable in local fields and pseudo-finite fields, Israel Journal of Mathematics, vol. 85 (1994), no. 1-3, pp. 203–262.CrossRefGoogle Scholar
[KP97]Kim, Byunghan and Pillay, Anand, Simple theories, Annals of Pure and Applied Logic, vol. 88 (1997), no. 2-3, pp. 149–164, Joint AILA-KGS Model Theory Meeting (Florence, 1995).CrossRefGoogle Scholar
[Mac75]Macintyre, Angus, Dense embeddings. I. A theorem of Robinson in a general setting, Model theory and algebra (A memorial tribute to Abraham Robinson), Lecture Notes in Mathematics, vol. 498, Springer, Berlin, 1975, pp. 200–219.CrossRefGoogle Scholar
[Ons02]Onshuus, Alf, þ-forkingin rosy theories, Ph.D. thesis, University of California at Berkeley, 2002.Google Scholar
[Ons06]Onshuus, Alf, Properties and consequences of thorn-independence, this Journal, vol. 71 (2006), no. 1, pp. 1–21.Google Scholar
[Pil96]Pillay, Anand, Geometric stability theory, Oxford Logic Guides, vol. 32, The Clarendon Press Oxford University Press, New York, 1996.CrossRefGoogle Scholar
[PP95]Pillay, Anand and Poizat, Bruno, Corps et chirurgie, this Journal, vol. 60 (1995), no. 2, pp. 528–533.Google Scholar
[She90]Shelah, S., Classification theory and the number of nonisomorphic models, second ed., Studies in Logic and the Foundations of Mathematics, vol. 92, North-Holland, Amsterdam, 1990.Google Scholar
[vdD88]van den Dries, Lou, Elimination theory for the ring of algebraic integers, Journal für die Reine und Angewandte Mathematik, vol. 388 (1988), pp. 189–205.Google Scholar
[vdD89]van den Dries, Lou, Dimension of definable sets, algebraic boundedness and Henselian fields, Annals of Pure and Applied Logic, vol. 45 (1989), no. 2, pp. 189–209.CrossRefGoogle Scholar
[vdDM90]van den Dries, Lou and Macintyre, Angus, The logic of Rumely's local-global principle, Journal für die Reine und Angewandte Mathematik, vol. 407 (1990), pp. 33–56.Google Scholar
[Wag00]Wagner, Frank O., Simple theories, Mathematics and its Applications, vol. 503, Kluwer Academic Publishers, Dordrecht, 2000.CrossRefGoogle Scholar