## Oberseminar mathematische Logik

### Organizers

- Prof. Dr. Peter Koepke
- Dr. Philipp Lücke

### Time and location

Tuesdays 16-18 in room N0.003, or by appointment (see below), Endenicher Allee 60.

### Talks

- 08 November (10.30 -12.00, Room SR 0.007): Ralf Schindler (Münster): MM
^{++}implies (∗)

For many years, forcing axioms and Woodin's**P**_{max}axiom (∗) were competing natural hypotheses which both decided the value of the continuum to be ℵ_{2}. The relationship of, say, Martin's Maximum with (∗) was a bit of a mystery. We show that Martin's Maximum^{++}implies Woodin's axiom (∗). This is joint work with David Asperó.

- 10 December: Wolfgang Wohofsky (Wien): A Sacks amoeba forcing preserving distributivity of P(omega) / Fin

In my talk, I would like to present joint work with Otmar Spinas, in which we show that it is consistent that h (the distributivity number of P(omega)/fin, in other words, the least number of maximal almost disjoint families without a common refinement) is strictly smaller than add(s_0) (i.e., the least number of Marczewski null sets whose union is not Marczewski null, where a set is Marczewski null if each perfect set has a perfect subset disjoint from it). More explicitly, we show that this relation between h and add(s_0) holds in the model obtained by a countable support iteration of length omega_2 of a specific kind of Sacks amoeba forcing which happens to have the pure decision and the Laver property, and therefore does not add Cohen reals. The model actually satisfies h=cov(M).