Titlebook: Set Theory; Techniques and Appli Carlos Augusto Prisco,Jean A. Larson,A. R. D. Math Conference proceedings 1998 Springer Science+Business M

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A Picaresque Approach to Set Theory Genealogyy of the participants (mainly set theorists) of the conferences in Cura?ao in 1995 and Barcelona in 1996 and of the contributors to this volume. It includes a partial list of students of A. Mostowski, some stories of mathematical beginnings and references for those interested in further study.

Wernickes-area

Recurrent Points and Hyperarithmetic Setsfinal set as those attacked by recurrent points, and use that characterisation to show that recurrent points must exist for any iteration with recursive data which does not stabilise at a recursive ordinal.

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Forcing AxiomsThis paper surveys combinatorial forcing axioms together with combinatorial and topological consequences and information about their consistency.

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Weak Forms of the Axiom of Choice and Partitions of Infinite SetsThere are many equivalent versions of the Axiom of Choice, and also many interesting consequences which are strictly weaker in terms of consistency strength. We examine various of these weaker forms of the Axiom of Choice and study how they are related to each other.

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Applications of ,-FunctionsOnce we start measuring mathematical objects using infinite cardinals we are led naturally into . which is a field about combinatorial constructions with associated two cardinals. Various internal and external questions can be asked, all related to the relation between the two associated cardinals, e.g.:

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