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

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References

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