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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, AUSTRIA E-mail: johannes.aquila@googlemail.com
ENRIQUE CASANOVAS
Affiliation:
DEPARTAMENTO DE LÓGICA, HISTORIA Y FILOSOFÍA DE LA CIENCIA, UNIVERSIDAD DE BARCELONA, MONTALEGRE 6, 08001 BARCELONA, SPAIN E-mail: e.casanovas@ub.edu
ANAND PILLAY
Affiliation:
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF NOTRE DAME, IN 46556, USA E-mail: a.pillay@leeds.ac.uk
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Abstract

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We prove two results about generically stable types p inarbitrary theories. The first, on existence of strong germs, generalizes resultsfrom [2] on stably dominated types. Thesecond is an equivalence of forking and dividing, assuming generic stability ofp (m) for all m. Weuse the latter result to answer in full generality a question posed by Hassonand Onshuus: If P(x) εS(B) is stable and does not fork overA then prestrictionA is stable. (They hadsolved some special cases.)

Keywords

Stable typesgenerically stable typesstrong germs

Information

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

References

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