Topic Archive: Pmax

CUNY Logic WorkshopFriday, October 18, 20132:00 pmGC 6417

Generic choice functions and ultrafilters on the integers

Miami University of Ohio

We will discuss a question asked by Stefan Geschke, whether the existence of a selector for the equivalence relation $E_0$ implies the existence of a nonprincipal ultrafilter on the integers. We will present a negative solution which is undoubtedly more complicated than necessary, using a variation of Woodin’s $mathbb{P}_{mathrm{max}}$. This proof shows that, under suitable hypotheses, if $E$ is a universally Baire equivalence relation on the reals, with countable classes, then forcing over $L(E,mathbb{R})$ to add a selector for $E$ does not add a nonprincipal ultrafilter on the integers.

Miami University of Ohio
Professor Larson (B.S. Dartmouth, Ph.D. UC Berkeley) conducts research in set theory, particularly on the topic of forcing and large cardinals.