You are here :
RANKS OF MAHARAM ALGEBRAS,
with Z. Perovic,
Solving a well-known problem of Maharam, Talagrand constructed an
exhaustive non uniformly exhaustive submeasure, thus also providing the first example
of a Maharam algebra that is not a measure algebra. To each exhaustive submeasure
one can canonically assign a certain countable ordinal, its exhaustivity rank. In this
paper, we use carefully constructed Schreier families and norms derived from them to
provide examples of exhaustive submeasures of arbitrary high exhaustivity rank. This
gives rise to uncountably many non isomorphic separable atomless Maharam algebras.
PFA AND PRECIPITOUSNESS OF THE NONSTATIONARY IDEAL,
We adapt the method of Neeman of forcing with side conditions to show
that PFA does not imply the precipitousness of the nonstationary ideal on $$\omega_1$$.
ITERATION OF SEMIPROPER FORCING REVISITED,
We present a method for iterating semiproper forcing
which uses side conditions and is inspired by the technique recently
introduced by Neeman.
PROPER FORCING REMASTERED,
with G. Venturi,
In these notes we present the method introduced by Neeman of generalized side conditions with two types of models.
We then discuss some applications: the Friedman-Mitchell poset for adding a club with finite conditions, Koszmider's forcing
construction of a strong chain of functions from \omega_1 to \omega_1, and the Baumgartner-Shelah forcing construction of
a thin very tall superatomic Boolean algebra.
A DIRECT PROOF OF THE FIVE ELEMENT BASIS THEOREM,
with G. Venturi,
We present a direct proof of the consistency of the existence
of a ve element basis for the uncountable linear orders. Our argument
is based on the approach of Larson, Koenig, Moore and Velickovic
and simplies the original proof of Moore.
OSCILLATIONS AND THEIR APPLICATIONS IN PARTIION CALCULUS,
with L. Fontanella,
Lectures notes taken by L. Fontanella from a tutorial given
at the 2nd Young Set Theory Workshop,
April 14-18, 2009 at the CRM in Bellaterra, Spain.
Jeux infinis et détermination,
Lecture notes from a course on Infinite games and determinacy tought at the Université de Paris - Diderot, 2009/2010 (in french).
To view or download PDF files you need Adobe® Acrobat® Reader® which can be downloaded for free from the Adobe Official Website ( 27.7MB).
You will also need a PostScript file viewer in order to view the PS files, such as Ghostview (UNIX,
distributed with ghostscript) and GSView (Windows) which can also read and display PDF files.