The *Hamburg Set Theory Workshop 2014* is part of the **ML** Colloquium of the *Arbeitsbereich Mathematische Logik und interdisziplinäre Anwendungen der Logik*. Everyone is cordially invited to attend. There will be an informal lunch in the student restaurant (Mensa) and an informal dinner.

11:00-12:00 | Andrew Brooke-Taylor (Bristol)Evasion of large cardinals |
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12:00-14:00 | LUNCH BREAK |

14:00-15:00 | Merlin Carl (Konstanz)Infinite Time Algorithmic Randomness |

15:00-15:30 | Break |

15:30-16:30 | Yurii Khomskii (Vienna)Suslin proper forcing and regularity properties |

16:30-17:00 | Break |

17:00-18:00 | Wolfgang Wohofsky (Vienna)Strong measure zero sets and their characterization via translations |

### Abstracts

Andrew Brooke-Taylor (Bristol)

*Evasion of large cardinals*

The evasion number **e** is a cardinal characteristic of the continuum introduced by Blass in connection with questions about homomorphisms of groups. However, the definition of **e** itself is very combinatorial, and generalises easily to larger cardinals. I will talk about lifting inequalities from the well-studied ω case up to a large cardinal κ, focusing especially on the consistency of **e**>**b** in this context. This is joint work with Jörg Brendle.

Merlin Carl (Konstanz)

*Infinite Time Algorithmic Randomness*

We consider algorithmic randomness for machine models of infinitary computations. We show that a theorem of Sacks, according to which a real *x* is computable from a randomly chosen real with positive probability iff it is recursive holds for many of these models, but is independent from **ZFC** for ordinal Turing machines. Furthermore, we define an analogue of ML-randomness for Infinite Time Register Machines and show that some classical results like van Lambalgen’s theorem continue to hold.

Yurii Khomskii (Vienna)

*Suslin proper forcing and regularity properties*

Recently, in joint work with Vera Fischer and Sy Friedman, we obtained a number of new results separating regularity properties on the Δ^{1}_{3}, Σ^{1}_{3} and Δ^{1}_{4} levels of the projective hierarchy. In this talk I will present some of the methods we used to obtain these results, focusing on the concept of “Suslin/Suslin+ proper forcing”, a strengthening of Shelah’s concept of proper forcing which only works for easily definable forcing notions, and which was a crucial technical ingredient in our proofs.

Wolfgang Wohofsky (Vienna)

*Strong measure zero sets and their characterization via translations*

The Galvin-Mycielski-Solovay theorem confirms a conjecture of Prikry saying that a set of reals is strong measure zero if and only if it can be translated away from each meager set. This connection gives rise to a variety of new “notions of smallness”. It is possible to generalize the theorem to arbitrary locally compact Polish groups. However, some amount of compactness seems to be necessary: we show that the theorem consistently fails for the Baer-Specker group **Z**^{ω}. This is joint work with Michael Hrusak and Ondrej Zindulka.