Reductions between Cardinal Characteristics of the Continuum
نویسندگان
چکیده
We discuss two general aspects of the theory of cardinal characteristics of the continuum, especially of proofs of inequalities between such characteristics. The first aspect is to express the essential content of these proofs in a way that makes sense even in models where the inequalities hold trivially (e.g., because the continuum hypothesis holds). For this purpose, we use a Borel version of Vojtáš’s theory of generalized Galois-Tukey connections. The second aspect is to analyze a sequential structure often found in proofs of inequalities relating one characteristic to the minimum (or maximum) of two others. Vojtáš’s max-min diagram, abstracted from such situations, can be described in terms of a new, higher-type object in the category of generalized Galois-Tukey connections. It turns out to occur also in other proofs of inequalities where no minimum (or maximum) is mentioned.
منابع مشابه
Reading Course: Set Theory Ws 2017
Excellent expository articles regarding the cardinal charactersitcs of the continuum are A. Blass, Combinatorial Cardinal Characteristics of the Continuum (see [2]) and T. Bartoszynski, Invariants of measure and category (see [1]). Both of those articles should be available on-line, but if you cannot access them, please contact me to get a copy. In addition, for those students in the class, who...
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