scholarly journals There are no very meager sets in the model in which both the Borel Conjecture and the dual Borel Conjecture are true

2016 ◽  
Vol 62 (4-5) ◽  
pp. 434-438
Author(s):  
Saharon Shelah ◽  
Wolfgang Wohofsky
Keyword(s):  
Borel Conjecture ◽  
Meager Sets

scholarly journals COUNTABLY PERFECTLY MEAGER SETS

2021 ◽  
pp. 1-17
Author(s):  
R. POL ◽  
P. ZAKRZEWSKI
Keyword(s):  
Meager Sets

On Lower and Semi-Lower Density Operators

2007 ◽  
Vol 14 (4) ◽  
pp. 661-671
Author(s):  
Jacek Hejduk ◽  
Anna Loranty
Keyword(s):  
Density Operator ◽  
Baire Property ◽  
Density Operators ◽  
Dense Sets ◽  
Meager Sets ◽  
Algebras Of Sets

Abstract This paper contains some results connected with topologies generated by lower and semi-lower density operators. We show that in some measurable spaces (𝑋, 𝑆, 𝐽) there exists a semi-lower density operator which does not generate a topology. We investigate some properties of nowhere dense sets, meager sets and σ-algebras of sets having the Baire property, associated with the topology generated by a semi-lower density operator.

The γ-borel conjecture

2004 ◽  
Vol 44 (4) ◽  
pp. 425-434 ◽  
Author(s):  
Arnold W. Miller
Keyword(s):  
Borel Conjecture

scholarly journals There are no $Q$-points in Laver’s model for the Borel conjecture

1980 ◽  
Vol 78 (1) ◽  
pp. 103-103 ◽  
Author(s):  
Arnold W. Miller
Keyword(s):  
Borel Conjecture

scholarly journals On Haar meager sets

2013 ◽  
Vol 160 (18) ◽  
pp. 2396-2400 ◽  
Author(s):  
Udayan B. Darji
Keyword(s):  
Meager Sets

scholarly journals Haar meager sets revisited

2016 ◽  
Vol 440 (2) ◽  
pp. 922-939 ◽  
Author(s):  
Martin Doležal ◽  
Martin Rmoutil ◽  
Benjamin Vejnar ◽  
Václav Vlasák
Keyword(s):  
Meager Sets

Products of Perfectly Meager Sets and Lusin's Function

1989 ◽  
Vol 107 (3) ◽  
pp. 811
Author(s):  
Janusz Pawlikowski
Keyword(s):  
Meager Sets

Finite support iteration and strong measure zero sets

1990 ◽  
Vol 55 (2) ◽  
pp. 674-677
Author(s):  
Janusz Pawlikowski
Keyword(s):  
Real Line ◽  
Measure Zero ◽  
Finite Support ◽  
The Real ◽  
Zero Sets ◽  
Strong Measure ◽  
Borel Conjecture ◽  
Strong Measure Zero ◽  
Finite Support Iteration

AbstractAny finite support iteration of posets with precalibre ℵ1 which has the length of cofinahty greater than ω1 yields a model for the dual Borel conjecture in which the real line is covered by ℵ1 strong measure zero sets.

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