Mon curriculum vitae comprenant une liste de mes publications / My curriculum
vitae, including a list of publications: cv.pdf.
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My main research subject is set theory. I have a particular interrest in set theory with a universal set. The most interesting theories (but not the only ones) in this area are the positive set theory (GPK^{+} and its extension) and the theory New Foundation (NF and NFU) of Quine.
The positive set theory GPK^{+} has been my major topic of interest. It has a comprehension scheme for positive formulas (where "positive" is taken in a rather liberal sense). Obviously this leads to the existence of a universal set V = { x | x = x } (the formula "x = x" being positive). One of the most interesting theorems about this theory is that GPK^{+}_{infinity} (GPK^{+} with a form of the axiom of infinity) is mutually interpretable with the Kelley-Morse class theory + the proper class of all ordinals is weakly compact.
The theory NF is the most known set theory with a universal set. It has a comprehension scheme for stratified formulas. Stratified formulas are formulas of the theory of types where we have "forgotten" the types. A lot of work has been done in this theory. The big remaining open question is to prove its consistency.
Let us mention also the paradoxical set theories and the Skala set theory. Some of the paradoxical set theories have links with the positive set theories. The Skala set theory is another theory with a universal set.
Another point of interest is the tree property for directed sets. This is a generalisation to directed sets of the classical tree property for cardinals in ZFC. This notion appears naturally in the construction of models for the positive set theory; but this topic is interesting in itself. One can even generalized this property for arbitrary ordered sets though the main applications of this notion are for directed sets.
Recently I have studied the property of forcing with the antifondation axiom AFA of M. Forti, F. Honsell et P.Aczel. The aim is to show that that the classical construction of forcing continue to works.