Veranstaltungsübersicht -- Sommersemester 2024

Dienstag,
2024-05-28
14:30 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Charlotte Bartnick: Stationarity in beautiful pairs

A type in a stable theory $T$ is stationary if it has a unique non-forking extension. By adding imaginary elements to a model of $T$, types over algebraically closed sets in the expanded structure become stationary. If $T$ does not eliminate imaginaries, the question arises whether types over algebraically closed subsets in the original model (real subsets) are also stationary.

After reviewing all the above notions, we will discuss this problem for the theory $T_P$ of beautiful pairs of models of a stable theory $T$ introduced by Poizat. By a result of Pillay and Vassiliev, this theory does not have (geometric) elimination of imaginaries if an infinite group is definable in $T$. We will prove that types over real algebraically closed sets in $T_P$ are stationary.

Dienstag,
2024-06-04
14:30 Uhr
Raum 404, Ernst-Zermelo-Str. 1
Hannes Jakob: Friedman's and other Reflection Properties

In 1975, Friedman introduced the property $F(\kappa)$, stating that every subset of $\kappa$ either contains or is disjoint from a closed set of ordertype $\omega_1$. Famously, this property follows from the power forcing axiom ``Martin's Maximum''. In this talk, we introduce posets which force the negation of this property and other related notions and investigate the patterns in which these properties can fail in connection to large cardinals.


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