Physical Sciences and Mathematics Commons^™

Cardinal Invariants And The Borel Tukey Order, Samuel Coskey

Samuel Coskey

Many proofs of inequalities between cardinal characteristics of the continuum are combinatorial in nature. These arguments can be carried out in any model of set theory, even a model of CH where the inequalities themselves are trivial. Thus, such arguments appear to establish a stronger relationship than a mere inequality. The Borel Tukey order was introduced by Blass in a 1996 article to address just this. Specifically, he observed that the combinatorial information linking two cardinal characteristics is often captured by a pair of Borel maps called a Borel Tukey morphism. The existence of a Borel Tukey morphisms between …