Left-distributive embedding algebras.
Lelek fan from a projective Fraïssé limit
We show that a natural quotient of the projective Fraïssé limit of a family that consists of finite rooted trees is the Lelek fan. Using this construction, we study properties of the Lelek fan and of its homeomorphism group. We show that the Lelek fan is projectively universal and projectively ultrahomogeneous in the class of smooth fans. We further show that the homeomorphism group of the Lelek fan is totally disconnected, generated by every neighbourhood of the identity, has a dense conjugacy...
Lengths of Submodule Chains Versus Krull Dimension in Non-Noetherian Modules.
Les boules peuvent-elles engendrer la tribu borélienne d'un espace métrisable non séparable ?
Les chaínes complêtes sont simplifiables à droite pour la multiplication ordinale
Les dérivations analytiques
Les dérivations en théorie descriptive des ensembles et le théorème de la borne
Les ensembles projectifs et analytiques [Book]
Les fonctions continues et la propriété de Baire
Les propriétés de réduction et de norme pour les classes de Boréliens
Less than many translates of a compact nullset may cover the real line
We answer a question of Darji and Keleti by proving that there exists a compact set C₀ ⊂ ℝ of measure zero such that for every perfect set P ⊂ ℝ there exists x ∈ ℝ such that (C₀+x) ∩ P is uncountable. Using this C₀ we answer a question of Gruenhage by showing that it is consistent with ZFC (as it follows e.g. from ) that less than many translates of a compact set of measure zero can cover ℝ.
Level by level equivalence and the number of normal measures over
We construct two models for the level by level equivalence between strong compactness and supercompactness in which if κ is λ supercompact and λ ≥ κ is regular, we are able to determine exactly the number of normal measures carries. In the first of these models, carries many normal measures, the maximal number. In the second of these models, carries many normal measures, except if κ is a measurable cardinal which is not a limit of measurable cardinals. In this case, κ (and hence also )...
Level by Level Inequivalence, Strong Compactness, and GCH
We construct three models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In the first two models, below the supercompact cardinal κ, there is a non-supercompact strongly compact cardinal. In the last model, any suitably defined ground model Easton function is realized.
Liaisons entre les S-relations et les relations de ferrers. Représentations
Life in the Sacks model
Limits of families of measure algebras
Lindelöf indestructibility, topological games and selection principles
Arhangel’skii proved that if a first countable Hausdorff space is Lindelöf, then its cardinality is at most . Such a clean upper bound for Lindelöf spaces in the larger class of spaces whose points are has been more elusive. In this paper we continue the agenda started by the second author, [Topology Appl. 63 (1995)], of considering the cardinality problem for spaces satisfying stronger versions of the Lindelöf property. Infinite games and selection principles, especially the Rothberger property,...
Linear extenders and the Axiom of Choice
In set theory without the Axiom of Choice ZF, we prove that for every commutative field , the following statement : “On every non null -vector space, there exists a non null linear form” implies the existence of a “-linear extender” on every vector subspace of a -vector space. This solves a question raised in Morillon M., Linear forms and axioms of choice, Comment. Math. Univ. Carolin. 50 (2009), no. 3, 421-431. In the second part of the paper, we generalize our results in the case of spherically...
Linear forms and axioms of choice
We work in set-theory without choice ZF. Given a commutative field , we consider the statement : “On every non null -vector space there exists a non-null linear form.” We investigate various statements which are equivalent to in ZF. Denoting by the two-element field, we deduce that implies the axiom of choice for pairs. We also deduce that implies the axiom of choice for linearly ordered sets isomorphic with .
Linear orders and MA + ¬wKH
I prove that the statement that “every linear order of size can be embedded in ” is consistent with MA + ¬ wKH.