EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXVII, No. 33, pp. 91–130 ()

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Rectangular axioms, perfect set properties and decomposition

J. Brendle, P. Larson and S. Todorcevic

Graduate School of Science and Technology, Kobe University, Kobe 657-8501, Japan
Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, USA
Universite Paris VII – C. N. R. S., UPRESA 7056, Paris 75251, Cedex 05, France

Abstract: We consider three combinatorial topics appearing in G\"{o}del's manuscript \emph{Some considerations leading to the probable conclusion that the true power of the continuum is $\aleph_{2}$}. These statements concern rectangular functions, perfect set properties, and covering properties of sets of reals. We consider these statements in light of more recent work on the set theory of the reals.

Keywords: Goedel's rectangular axioms, the cardinality of the continuum, perfect-set properties

Classification (MSC2000): 03E50, 03E17

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Electronic fulltext finalized on: 7 Sep 2008. This page was last modified: 20 Jun 2011.

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