Event Detail

This talk is to show off the versatility of random real forcing for obtaining relative consistency results (and some positive results) over a wide variety of theories. When one wishes to find the nicest way the reals can behave regarding some problem, it is common to first analyze the question in the Solovay model or even determinacy models for their strong regularity properties, at the expense of large cardinal strength. But these constructions can often be carried out in random real extensions, achieving relative consistency over ZF, Z, and nth order arithmetic, while also maintaining fragments of choice far beyond DC.

I’ll go over some of the key features of random real forcing and identify some commonalities with and advantages over Cohen forcing. Then I will discuss some recent results that rely on random reals, pertaining to projective models of arithmetic, planar combinatorics, and prediction puzzles.