Sequential Composition and Baire Category
by
Andreas Blass
University of Michigan, Ann Arbor

Many cardinal characteristics of the continuum are norms of relations on the reals, and many of the provable inequalities between characteristics arise from Borel morphisms between corresponding relations. Inequalities that involve three characteristics, like add(B) >= min cov(B), b, often arise from Borel morphisms out of sequential compositions of relations. A natural approach to justifying the use of sequential composition in these situations (rather than simpler constructions that would, if the necessary morphisms existed, yield the same inequalities) would be to exhibit a Borel morphism in the other direction. Unfortunately, it is not obvious how to define the notion of a Borel morphism into a sequential composition. In this talk, I shall explain what the difficulty is, propose a solution, explain where the solution came from, and, if time permits, explain how to construct a Borel morphism in the reverse direction for the particular inequality exhibited above.

Date received: March 13, 2002