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Preprints



RANKS OF MAHARAM ALGEBRAS
with Z. Perovic,



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Abstract

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


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Abstract

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


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Abstract

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,


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Abstract

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,


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Abstract

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 simpli es the original proof of Moore.



OSCILLATIONS AND THEIR APPLICATIONS IN PARTIION CALCULUS
with L. Fontanella,


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Abstract

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.


Notes



Jeux infinis et détermination


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Abstract

Lecture notes from a course on Infinite games and determinacy tought at the Université de Paris - Diderot, 2009/2010 (in french).
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