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30 June 2005 Small sets in convex geometry and formal independence over ZFC
Menachem Kojman
Abstr. Appl. Anal. 2005(5): 469-488 (30 June 2005). DOI: 10.1155/AAA.2005.469


To each closed subset S of a finite-dimensional Euclidean space corresponds a σ-ideal of sets 𝒥(S) which is σ-generated over S by the convex subsets of S. The set-theoretic properties of this ideal hold geometric information about the set. We discuss the relation of reducibility between convexity ideals and the connections between convexity ideals and other types of ideals, such as the ideals which are generated over squares of Polish space by graphs and inverses of graphs of continuous self-maps, or Ramsey ideals, which are generated over Polish spaces by the homogeneous sets with respect to some continuous pair coloring. We also attempt to present to nonspecialists the set-theoretic methods for dealing with formal independence as a means of geometric investigations.


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Menachem Kojman. "Small sets in convex geometry and formal independence over ZFC." Abstr. Appl. Anal. 2005 (5) 469 - 488, 30 June 2005.


Published: 30 June 2005
First available in Project Euclid: 25 July 2005

zbMATH: 1140.03034
MathSciNet: MR2201038
Digital Object Identifier: 10.1155/AAA.2005.469

Rights: Copyright © 2005 Hindawi

Vol.2005 • No. 5 • 30 June 2005
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