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DEFINABLE AND INVARIANT TYPES IN ENRICHMENTS OF NIP THEORIES

Published online by Cambridge University Press:  21 March 2017

SILVAIN RIDEAU  and
PIERRE SIMON
SILVAIN RIDEAU
Affiliation:
UNIVERSITY OF CALIFORNIA, BERKELEY MATHEMATICS DEPARTMENT, EVANS HALL BERKELEY, CA, 94720-3840, USAE-mail: silvain.rideau@berkeley.eu
PIERRE SIMON
Affiliation:
UNIV LYON, UNIVERSITÉ CLAUDE BERNARD LYON 1 CNRS UMR 5208, INSTITUT CAMILLE JORDAN 43 BLVD. DU 11 NOVEMBRE 1918 F-69622 VILLEURBANNE CEDEX, FRANCEE-mail: simon@math.univ-lyon1.fr
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Abstract

Let T be an NIP ${\cal L}$-theory and $\mathop T\limits^\~ $ be an enrichment. We give a sufficient condition on $\mathop T\limits^\~$ for the underlying ${\cal L}$-type of any definable (respectively invariant) type over a model of $\mathop T\limits^\~$ to be definable (respectively invariant). These results are then applied to Scanlon’s model completion of valued differential fields.

Keywords

model theoryNIP theoriesdefinable typesinvariant typesreductvalued fields with a contractive derivation
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 1 , March 2017 , pp. 317 - 324
Copyright
Copyright © The Association for Symbolic Logic 2017 

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References

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