Location: SR1D
Time: Friday 4:15-5:45pm
 

• April 13th - Nikolina Barišić: Hyper Fine Strucure Theory

  Abstract: After giving a small overview of the constructible universe, I am going to introduce the
  notion of constructible operations.
  The main part of my talk will be centered on Condensation theorem, which, in rough,
  states the following: assuming \(X \subseteq L\) is constructibly closed and given \(\pi \colon X \prec M\) be the
  Mostowski collapse of \(X\) to the transitive set \(M\), then there is an ordinal \(\alpha\) such that
  \(M = L_{\alpha}\)
  Consequences / corrolaries:
  a) the standard condensation lemma holds also for successor levels of the \(L\)-hierarchy
  b) elementarity in constructible levels with respect to the additional predicates \(I, N\) and \(S\)
  is just the same as elementarity without them.

• May 5th - Philipp Lücke: Squares, ascent paths, and chain conditions

  Abstract:  Given an uncountable regular cardinal \(\kappa\), Todorčević's square principle \(\square(\kappa)\) asserts the existence of a non-threadable coherent club sequence of length \(\kappa\).
  In my talk, I want to present several new constructions of combinatorial objects from this principle.
  In particular, I will show that for all \(\kappa>\omega_1\), the principle \(\square(\kappa)\) implies the existence of a non-specializable \(\kappa\)-Aronszajn tree as well as a failure of the countable productivity of the \(\kappa\)-Knaster property.
  All of these constructions rely on a result that shows that \(\square(\kappa)\) implies an indexed version of the principle \(\square(\kappa,\lambda)\).
  
  This is joint work with Chris Lambie-Hanson (Bar-Ilan).
• June 8th - Jonas Fox: Starke Logiken und Innere Modelle
  
  Abstract: Mein Vortrag beschäftigt sich mit der Konstruktion innerer Modelle zwischen \(L\) und \(HOD\). Dabei wird in der Konstruktion von \(L\) die Logik erster Stufe durch stärkere Logiken ersetzt. Im Hauptteil des Vortrages wird konkret die Logik erster Stufe durch Hinzufügen eines Kofinalitätsquantors erweitert und das dadurch konstruierte innere Modell \(C^{*}\) diskutiert. Wichtige Ergebnisse sind beispielsweise, dass das Dodd-Jensen-Core-Modell in \(C^{*}\) enthalten ist und dass eine Erweiterung von \(C^{*}\) unter Voraussetzung bestimmter großer Kardinalzahlen die Kontinuumshypothese erfüllt.
• June 13th - Jonas Fox: Starke Logiken und Innere Modelle (Fortsetzung)