Continuous Ramsey theory on Polish spaces and covering the plane by functions

S Geschke, M Goldstern, M Kojman - arxiv preprint math/0205331, 2002‏ - arxiv.org
We investigate the Ramsey theory of continuous pair-colorings on complete, separable
metric spaces, and apply the results to the problem of covering a plane by functions. The …

Weak Borel chromatic numbers

S Geschke - Mathematical Logic Quarterly, 2011‏ - Wiley Online Library
Given a graph G whose set of vertices is a Polish space X, the weak Borel chromatic number
of G is the least size of a family of pairwise disjoint G‐independent Borel sets that covers all …

A dual open coloring axiom

S Geschke - Annals of Pure and Applied Logic, 2006‏ - Elsevier
We discuss a dual of the Open Coloring Axiom (OCA [ARS]) introduced by Abraham et al.[U.
Abraham, M. Rubin, S. Shelah, On the consistency of some partition theorems for continuous …

Borel chromatic numbers in models of set theory

M Fernandes Gaspar - 2022‏ - ediss.sub.uni-hamburg.de
In this work, we study the behavior of definable graphs on Polish spaces in various models
of set theory. More specifically, we investigate their Borel chromatic numbers, one of the so …

The breadth of constructibility degrees and definable Sierpi\'nski's coverings

A Andretta, L Notaro - arxiv preprint arxiv:2408.10182, 2024‏ - arxiv.org
arxiv:2408.10182v1 [math.LO] 19 Aug 2024 Page 1 arxiv:2408.10182v1 [math.LO] 19 Aug 2024
THE BREADTH OF CONSTRUCTIBILITY DEGREES AND DEFINABLE SIERPINSKI’S …

Covering an uncountable square by countably many continuous functions

W Kubiś, B Vejnar - Proceedings of the American Mathematical Society, 2012‏ - ams.org
We prove that there exists a countable family of continuous real functions whose graphs,
together with their inverses, cover an uncountable square, ie a set of the form $ X\times X …

[PDF][PDF] Cardinal invariants from continuous Ramsey theory

TV Weinert‏ - Citeseer
The topos of this research can be traced back to 1878 when the mathematician Georg
Cantor stated his famous continuum problem. He asked whether every uncountable set of …

Small sets in convex geometry and formal independence over ZFC

M Kojman - Abstract and Applied Analysis, 2005‏ - Wiley Online Library
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 …

[PDF][PDF] CONVEX GEOMETRY, CONTINUOUS RAMSEY THEORY, AND IDEALS GENERATED BY GRAPHS OF FUNCTIONS

S GESCHKE - 2004‏ - math.uni-hamburg.de
CONVEX GEOMETRY, CONTINUOUS RAMSEY THEORY, AND IDEALS GENERATED BY
GRAPHS OF FUNCTIONS 1. Convexity numbers of closed sets in R Page 1 CONVEX …

[معلومات الإصدار][C] continuous Ramsey theory

TV Weinert