Graduate seminar on logic (S4A3)
- Prof. Dr. Peter Koepke
Time and place
Tuesdays 14:15-16:00 at seminar room C, Beringstrasse 1 .
- 21 October, Ioanna Dimitriou "How to make and use symmetric models".
- We'll go through my chapter on symmetric models, understanding how exactly these symmetric models are created, what is the basic idea and tools behind this construction, and discussing in detail the very important property a symmetric model might have: satisfying the symmetric product lemma. We'll see as many interesting examples as time permits. This will be a blackboard talk.
- 28 October, Ioanna Dimitriou "Examples of symmetric models with large cardinals "
- This time we saw Jech's model where ω1 is measurable and defined the partial order for a set sized version of Gitik's model where all uncountable cardinals are singular.
- 4 November, Ioanna Dimitriou "Examples of symmetric models with large cardinals 2"
- Now we're at a set sized version of the Gitik model in "All uncountable cardinals can be singular". Last time we saw the definition of the partial order. This time we'll construct the symmetric model and prove the symmetric product lemma for it.
- 11 November, Ioanna Dimitriou "The Prikry lemma for symmetric tree-Prikry forcing and more"
- So far we built a symmetric model with tree-Prikry forcing using a ρ-long sequence of strongly compact cardinals and we proved the symmetric product lemma for it. Next we'll see that a symmetric version of the Prikry lemma holds.
- 18 November Ioanna Dimitriou "Properties of the set sized Gitik model" and Jip Veldman "On ordinal definability"
- Dimitriou: Finally we'll show that all the κα are preserved and that every ordinal in the interval (ω,η] is now singular.
Veldman: In this talk I will present various inner models that can be defined using ordinal definability and then formalize these constructions within ZF or ZFC.
25 November, Ioanna Dimitriou "Applications of symmetric models; choiceless Erdös cardinals"
- In this talk we'll look at Erdös cardinals. We'll see two symmetric models, one that gives us an Erdös being a successor of a regular cardinal and one that gives us an Erdös being a successor of a singular. The first one is a symmetric Levy collapse and the second a symmetric
strongly compactPrikry forcing. We'll use the techniques from the previous talks, so the proofs are not going to be so complicated any more.
2 December Ioanna Dimitriou "More about symmetric models"
- 9 December Jip Veldman "Approximation models"
15 December talk cancelled
6 January talk cancelled
13 January Jip Veldman "Approximation models 2"
20 January Jip Veldman "Approximation models 3"