Department of Mathematics|
University of Florida
Gainesville, FL 32611-8105
In the spring term 2012, I teach a descriptive set theory course MAT6932 (the take home exam is posted here ) and a honors calculus MAC3474, section 7498 .
In the event that my students want to check my credentials
before enrolling in my classes, here is my resume .
Recent or not so recent papers and preprints:
- My book "Forcing Idealized" has appeared, Cambridge Tracts in Mathematics 174, ISBN 0521874262, ISBN-13 978-0-521-87426-7, order
- A preprint version of a new book Canonical Ramsey Theory on Polish Spaces , with Vladimir Kanovei and Marcin Sabok, to appear in Cambridge University Press
- A preprint, Overspill and forcing, connecting the phenomenon of overspill in descriptive set theory with a forcing preservation theorem, with an application to harmonic analysis
- Preservation of P-points is equivalent to a Fubini-type property in definable idealized forcing, Preserving P-points in definable forcing
- For a given sigma-ideal, the sub-sigma-ideal generated by closed sets gives rise to a quotient forcing with properties
reminiscent of the original quotient, Forcing properties of ideals generated by closed sets, with Marcin Sabok
- A joint paper with Saharon Shelah Ramsey theorems for products of finite sets with submeasures, utilizing the creature technology to prove a Polish partition theorem
- The n-localization property is preserved under the countable support iteration of definable proper forcing, while
it is not preserved in iterations of arbitrary proper forcings, n-localization property in iterations.
- The weak Laver property is preserved under the countable support iteration of definable forcing in conjunction
with the bounding property, but not without it. Moreover, it is equivalent to the Fubini property with
all definably sigma-centered ideals, and among these there is a key one to consider (and it is not the Hechler forcing, it is something
a little different). Here.
- I recently resolved the pinned equivalence conjecture, Pinned equivalence relations