Department of Mathematics                           University of Haifa
 
                  Special Infinite Combinatorics Seminar
 
Speaker: Assaf Rinot
         The Fields Institute, Toronto
 
Title:   Strong colorings:
           the study of the failure of generalized Ramsey statements
 
Date:    Thursday, June 7, 2012
 
Place:   Room 665 of the Science & Education Building, Univ. of Haifa
 
Time:    14:10
 
   ===>   NOTE  special day, time , and room !!  <===
 
          Abstract:
 
       A strong coloring from X to Y is a function that transforms
 relatively thin subsets of X into relatively fat subsets of Y. The
 first example of a strong coloring is due to Sierpinski (1933), who
 constructed a function from R^2 into {0,1} with the (anti-Ramsey)
 property that the image of any uncountable square A^2 equals {0,1}.
 In the mid 1960's, Erdos and his collaborators, utilized the Continuum
 Hypothesis to construct a function from R^2 into R with the remarkable
 property that the image of any uncountable square A^2 equals R. Ever
 since, the study of strong colorings has focused on constructing
 colorings for various sets without the aid of any additional set
 theoretic axioms.
     In this talk, we shall survey the history of the theory of strong
 colorings, their interaction with the L-Space and S-Space problems,
 and report on our recent contributions to the theory.
 
 This is joint work with Stevo Todorcevic.
 
---------------------------------------------------------
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: David Blanc   <blanc@math.haifa.ac.il>