Permitted trigonometric thin sets and infinite combinatorics
We investigate properties of permitted trigonometric thin sets and construct uncountable permitted sets under some set-theoretical assumptions.
Planting Kurepa trees and killing Jech-Кunen trees in a model by using one inaccessible cardinal
By an - tree we mean a tree of power and height . Under CH and we call an -tree a Jech-Kunen tree if it has κ-many branches for some κ strictly between and . In this paper we prove that, assuming the existence of one inaccessible cardinal, (1) it is consistent with CH plus that there exist Kurepa trees and there are no Jech-Kunen trees, which answers a question of [Ji2], (2) it is consistent with CH plus that there only exist Kurepa trees with -many branches, which answers another...
Primariness of some spaces of continuous functions.
Progrès récents sur l’hypothèse du continu
Les travaux récents de Woodin ont considérablement renouvelé la théorie des ensembles en lui apportant une intelligibilité globale et en restaurant son unité. Pour la première fois, ses résultats ouvrent une perspective réaliste de résoudre le problème du continu, et, à tout le moins, ils établissent le caractère irréfutablement signifiant et précis de celui-ci.
Propriété de Nikodym et propriété de Grothendieck
Rapid ultrafilter need not be Q-point
Rectangular axioms, perfect set properties and decomposition
Relations between ß X / X and a Certain Subspace of ... X.
Remarks on powers of lattices
Remarks on products of σ-ideals
Representation of functions of two variables as sums of rectangular functions, I
Rings of Real-Valued Continuous Functions. II.
Rudin's Dowker space in the extension with a Suslin tree
We introduce a generalization of a Dowker space constructed from a Suslin tree by Mary Ellen Rudin, and the rectangle refining property for forcing notions, which modifies the one for partitions due to Paul B. Larson and Stevo Todorčević and is stronger than the countable chain condition. It is proved that Martin's Axiom for forcing notions with the rectangle refining property implies that every generalized Rudin space constructed from Aronszajn trees is non-Dowker, and that the same can be forced...
Sacks reals and Martin's axiom
Selection from Upper Semi-Continuous Compact-Valued Mappings.
Sequential completeness and -sequential completeness are different
Set mappings on generalized linear continua
Sets with no uncountable Blackwell subsets
Set-theoretic constructions of two-point sets
A two-point set is a subset of the plane which meets every line in exactly two points. By working in models of set theory other than ZFC, we demonstrate two new constructions of two-point sets. Our first construction shows that in ZFC + CH there exist two-point sets which are contained within the union of a countable collection of concentric circles. Our second construction shows that in certain models of ZF, we can show the existence of two-point sets without explicitly invoking the Axiom of Choice....
Small almost free modules with prescribed topological endomorphism rings