Topology + Foundations
32nd Summer Conference on Topology and Its Applications
Consider the statement that every uncountable set of reals can be surjected onto R by a Borel function. This is implied by the statement that every uncountable set of reals has a perfect subset. It is also implied by a new statement D which we will discuss: for each real a there is a Borel function fa : RtoR and for each function g : RtoR there is a countable set G(g) of reals such that the following is true: for each a in R and for each function g : R to R, if fa is disjoint from g, then a is in G(g). We will show that D follows from ZF +AD+ whereas the negation of D follows from ZFC.
Copyright © 2017, the Author
Hathaway, Daniel, "Disjoint Infinity Borel Functions" (2017). Summer Conference on Topology and Its Applications. 10.