Mathematisches Forschungsinstitut Oberwolfach Report No. 55/2005 Set Theory

Abstract. This meeting covered all important aspects of modern Set Theory, including large cardinal theory, combinatorial set theory, descriptive set theory, connections with algebra and analysis, forcing axioms and inner model theory. The presence of an unusually large number (19) of young researchers made the meeting especially dynamic. Mathematics Subject Classification (2000): 03Exx. Introduction by the Organisers This meeting was organised by Sy-David Friedman (University of Vienna), Menachem Magidor (Hebrew University, Jerusalem) and Hugh Woodin (University of California, Berkeley). Largely due to the generous EU support for the meeting, we were able to invite an unusually large number of young researchers (at mos

MATHEMATICAL LOGIC QUARTERLY www.mlq-journal.org A Journal for Mathematical Logic, Foundations of Mathematics, and Logical Aspects of Theoretical Computer Science M L Q Editors Armin Hemmerling, Greifswald (Managing) Klaus Ambos-Spies, HeidelbergK laus Me

A survey of the isomorphic submodels of Vω, the set of hereditarily finite sets. In the usual language of set theory, Vω has 2 ℵ 0 isomorphic submodels. But other set-theoretic languages give different systems of submodels. For example, the language of adjunction allows only countably many isomorphic submodels of Vω