Papers/Notes

  • Rachid Atmai, "An analysis of the models L[T2n]" pdf, accepted for publication in the Journal of Symbolic Logic.

    • The paper is about establishing the uniqueness of these models. The models are then characterized using inner model theory and it is shown that the GCH holds in L[T2n] for every natural number n. These results extend Hjorth's results on L[T2] and are a counterpart to Becker-Kechris analysis of L[T2n+1] and Steel's result on the GCH in L[T2n+1]

  • Rachid Atmai and Grigor Sargsyan, "The HOD up to ADR+Theta is measurable" pdf, submitted.

    • The paper is about computing the HOD of a determinacy model of the form L(P(R)) below ADR+Theta is measurable.

    Computing HOD's of models of axioms in the Solovay hierarchy is one of the main problem in inner model theory. The HOD's of models of determinacy turn out to be canonical models with fine structural properties in inner models theory. Recently Sargsyan has computed the HOD up to LSA, which is the boundary of what's known in terms of determinacy axioms.

  • Rachid Atmai and Steve Jackson, "A classification of projective algebras in L(R)" pdf, submitted.

    • This paper takes up the task of classifying projective-like hierarchies by properties of their associated Wadge ordinal. Type 4 hierarchies are characterized by a combinatorial property of their Wadge ordinal, solving an old conjecture of Kechris. Steel's conjecture on pointclasses fails, but several closure properties are established for the Steel pointclass at the base of a type 3 hierarchy.

  • Rachid Atmai and Steve Jackson, "Club version of the Kechris-Martin theorem and lightface scales" pdf, submitted

    • In this paper, we produce new techniques to construct lightface scales. In particular this produces a lightface scale analysis under ZF+AD using Jackson's notion of stability of trees. The notion of a stable tree is introduced in this note of Steve Jackson: Jackson notes

  • Rachid Atmai, "Contributions to descriptive set theory." pdf

    • this is my phd thesis.

  • Rachid Atmai, "Determinacy, consistency result in ZFC and effective counterexamples to the CH", in preparation.

    • In this work we try to establish the consistency of ZFC statements from determinacy principles

  • Rachid Atmai, "Supercompactness of omega_1 and LSA from the determinacy of long games", in preparation.

  • Rachid Atmai, Sy David Friedman and Yurii Khomski "Absoluteness and regularity properties for sets of reals", in preparation.