Wednesday, December 10 from 3 to 4pm

*Room*: Math 226

*Speaker*: Andrés Caicedo (BSU)

*Title*: Co-analytic uniformization

*Abstract*: It is an easy consequence of the axiom of choice that if X is an arbitrary set and R is a binary relation on X (a subset of $X^2$) then R admits a *uniformization*, that is, there is a function f whose domain is $\{x \in X : \text{there is a } y \in X \text{ with } x R y\}$ and such that for all x in its domain, x R f(x).

If X is the set of reals, and R is a reasonably definable relation, one might expect that the existence of such a function f can actually be established without using the axiom of choice.

We sketch a classical result independently due to Novikov and Kondo showing that this is indeed the case if R is Borel (and even if it is “slightly” more complicated than Borel).

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