TITLE: Transfinite belief in rationality. SPEAKER: Jonathan Zvesper ABSTRACT: We generalise a result from the literature, that says that playing a strategy that survives m+1 rounds of iterated elimination of non-optimal strategies is equivalent to rationality and m-th level mutual belief of rationality. In order to generalise this to infinite games, relational epistemic models do not suffice. -- In relational models, if for every finite m there is mutual belief of degree m in a proposition E, then for every ordinal a there is mutual belief of degree a in E. In order to separate finitary common belief from transfinite common belief, we use neighbourhood models, in particular we prove a generalisation of the mentioned theorem for the case of topological models and monotonic optimality operators. The idea of using topological epistemic models comes from [van Benthem and Sarenac, 2004], and the lattice-theoretic view on optimality operators from [Apt, 2007]. [Apt, 2007] Krzysztof R. Apt. Epistemic analysis of strategic games with arbitrary strategy sets. Proceedings of TARK 2007. [Benthem and Sarenac, 2004] Johan van Benthem and Darko Sarenac. The geometry of knowledge. In Aspects of Universal Logic, volume 17 of Travaux Log, pages 1--31, 2004.