Dipartimento di Matematica, Sala Seminari.<\/p>\n
It is well known that in a stable theory, all types are definable. In an unstable context, we can ask (like Cubides and Delon in [CD]) over which models $M$ of a given theory all types are definable. These models are exactly the models which are stably embedded in all elementary extensions (SE for short).<\/p>\n
In this talk, we will try to understand SE ordered abelian groups. For this, we will restrict our study to a well-behaved subclasse $\\mathcal{C}$ for which we will describe a language of (relative) quantifier elimination derived from the language of Clukers and Halupczok [CH]. Then, we will state our main result, which has the form of a transfer principle: an ordered abelian group in $\\mathcal{C}$ is SE if and only if it is maximal, the spine is SE and the regular classes are SE.<\/p>\n
This is a joint work with Martina Liccardo (University of Naples) and Martin Hils (University of M\u00fcnster).<\/p>\n
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[CD] Cubides Delon, Definable types in algebraically closed valued fields, 2016, MLQ. Mathematical Logic Quarterly<\/p>\n
[CH] Cluckers Halupczok, Quantifier elimination in ordered abelian groups, 2011, Confluentes Math.<\/p>\n
Further information is available on the event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":" It is well known that in a stable theory, all types are definable. In an unstable context, we can ask (like Cubides and Delon in [CD]) over which models $M$ of a given theory all types are definable. These models are exactly the models which are…<\/p>\n