Small sets in convex geometry and formal independence over ZFC

Menachem Kojman
2005 Abstract and Applied Analysis  
To each closed subsetSof a finite-dimensional Euclidean space corresponds aσ-ideal of sets𝒥 (S)which isσ-generated overSby the convex subsets ofS. The set-theoretic properties of this ideal hold geometric information about the set. We discuss the relation ofreducibilitybetween 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
more » ... s 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.
doi:10.1155/aaa.2005.469 fatcat:y3hxbtg5tva5pbj3dqabsys4bm