Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-22T01:41:52.806Z Has data issue: false hasContentIssue false
  • English
  • Français

GENERIC STABILITY AND STABILITY

Published online by Cambridge University Press:  17 April 2014

HANS ADLER ,
ENRIQUE CASANOVAS  and
ANAND PILLAY
HANS ADLER
Affiliation:
KURT GÖDEL RESEARCH CENTER FOR MATHEMATICAL LOGIC, HRINGER STRAßE 25, 1090 WIEN, AUSTRIAE-mail:[email protected]
ENRIQUE CASANOVAS
Affiliation:
DEPARTAMENTO DE LÓGICA, HISTORIA Y FILOSOFÍA DE LA CIENCIA, UNIVERSIDAD DE BARCELONA, MONTALEGRE 6, 08001 BARCELONA, SPAINE-mail:[email protected]
ANAND PILLAY
Affiliation:
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF NOTRE DAME, IN 46556, USAE-mail:[email protected]
Get access Rights & Permissions [Opens in a new window]

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.)

Keywords

Stable typesgenerically stable typesstrong germs
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 1 , March 2014 , pp. 179 - 185
Copyright
Copyright © Association for Symbolic Logic 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

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.Google Scholar
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.Google Scholar
Hasson, A. and Onshuus, A., Stable types in rosy theories. this Journal, vol. 75 (2010), no. 4, pp. 1211–1230.Google Scholar
Hrushovski, E. and Pillay, A., On NIP and invariant measures. Journal of the European Mathematical Society, vol. 13 (2011), pp. 1005–1061.Google Scholar
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. 189–211.Google Scholar
Shelah, S., Classification theory for elementary classes with the dependence property—A modest beginning. Scientiae Mathematicae Japonicae, vol. 59 (2004), no. 2, pp. 265–316.Google Scholar
Poizat, B., A course in model theory. Springer-Verlag, New York, 2000.Google Scholar