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A determinacy theorem proved using Martin's Axiom at the first uncountable cardinal
- Prelegent(ci)
- Matteo Mio
- Afiliacja
- Centre for Mathematics and Computer Science, Amsterdam
- Termin
- 6 listopada 2013 16:15
- Pokój
- p. 5050
- Seminarium
- Seminarium „Topologia i teoria mnogości”
Two players games of infinite duration (Gale-Stewart games) have come to play an important role in Computer Science. A game, typically played on a graph representing the state-to-state transitions of a program, is constructed in such a way that Player I wins if and only if the program exhibits good behavior against any potentially malicious interaction with an hostile environment (represented by Player II). Several variants of Gale-Stewart games (e.g., incorporating probabilistic choices) have been studied to model larger classes of problems.
In
this talk I will discuss a novel class of games which I introduced in
my PhD thesis. Interestingly, the Determinacy theorem is proven in
ZFC+MA_\aleph_1. I will also report on recent attempts, explored with Henryk Michalewski and PhD students Tomek Gogacz and Michał Skrzypczak, to prove the result in ZFC alone.
