Skip to main content
×
×
Home

GENERIC STABILITY AND STABILITY

  • HANS ADLER (a1), ENRIQUE CASANOVAS (a2) and ANAND PILLAY (a3)
Abstract
Abstract

We prove two results about generically stable types p in arbitrary theories. The first, on existence of strong germs, generalizes results from [2] on stably dominated types. The second is an equivalence of forking and dividing, assuming generic stability of p (m) for all m. We use the latter result to answer in full generality a question posed by Hasson and Onshuus: If P(x) ε S(B) is stable and does not fork over A then prestrictionA is stable. (They had solved some special cases.)

Copyright
References
Hide All
[1] Casanovas E., More on NIP and Related Topics, September 2011. Lecture Notes of Model Theory Seminar, University of Barcelona, available at http://www.ub.edu/modeltheory/documentos/nip2.pdf.
[2] Haskell D., Hrushovski E., and Macpherson D., Stable domination and independence in algebraically closed valued fields, Lecture Notes in Logic, vol. 30. Cambridge University Press, Cambridge, 2008.
[3] Hasson A. and Onshuus A., Stable types in rosy theories. this Journal, vol. 75 (2010), no. 4, pp. 12111230.
[4] Hrushovski E. and Pillay A., On NIP and invariant measures. Journal of the European Mathematical Society, vol. 13 (2011), pp. 10051061.
[5] Pillay A. and Tanović P., Generic stability, regularity, and quasi-minimality, Models, logics and higher-dimensional categories, vol. 53, CRM Proceedings and Lecture Notes, AMS, Providence, RI, 2011, pp. 189211.
[6] Shelah S., Classification theory for elementary classes with the dependence property—A modest beginning. Scientiae Mathematicae Japonicae, vol. 59 (2004), no. 2, pp. 265316.
[7] Poizat B., A course in model theory. Springer-Verlag, New York, 2000.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 14 *
Loading metrics...

Abstract views

Total abstract views: 87 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd February 2018. This data will be updated every 24 hours.