Omar Selim: More on exhaustive pathological submeasures

Data: quarta-feira, 08 de outubro de 2014, às 10h30

Sala: 242-A

Palestrante: Omar Selim, IME-USP

Título: More on exhaustive pathological submeasures

Resumo: Continuing from last week, I will give another proof that the ground model reals become small in extensions of exhaustive pathological submeasures. I will then introduce Talagrand's counter example to Maharam's problem and while doing so describe some of its absoluteness properties. From this one very quickly obtains the result that the collection of random reals in any such extension is measured as zero by Talagrand's submeasure.

Omar Selim: Ground model reals in extensions of pathological continuous submeasures

Data: quarta-feira, 01 de outubro de 2014, às 10h30

Sala: 242-A

Palestrante: Omar Selim, IME-USP

Título: Ground model reals in extensions of pathological continuous submeasures

Resumo: I will present a result from my thesis that says that the collection of ground model reals in any forcing extension due to a pathological and continuous submeasure is both Lebesgue null and meagre. This is analogous to the classical results that in the random extension the ground model reals are meagre and in the Cohen extension the ground model reals are Lebesgue null. I will try to give at least one full proof that only assumes forcing as a black box.