Borel Conjecture, dual Borel Conjecture, and other variants of the Borel Conjecture

2020 ◽  
pp. 135-227
Author(s):  
Wolfgang Wohofsky
Keyword(s):  
Borel Conjecture

The γ-borel conjecture

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

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.

scholarly journals Borel conjecture and dual Borel conjecture

2013 ◽  
Vol 366 (1) ◽  
pp. 245-307 ◽  
Author(s):  
Martin Goldstern ◽  
Jakob Kellner ◽  
Saharon Shelah ◽  
Wolfgang Wohofsky
Keyword(s):  
Borel Conjecture

scholarly journals The Borel Conjecture for hyperbolic and CAT(0)-groups

2012 ◽  
Vol 175 (2) ◽  
pp. 631-689 ◽  
Author(s):  
Arthur Bartels ◽  
Wolfgang Lück
Keyword(s):  
Borel Conjecture

Strong measure zero sets and rapid filters

1988 ◽  
Vol 53 (2) ◽  
pp. 393-402 ◽  
Author(s):  
Jaime I. Ihoda
Keyword(s):  
Measure Zero ◽  
Zero Sets ◽  
Strong Measure ◽  
Borel Conjecture ◽  
Strong Measure Zero

AbstractWe prove that cons(ZF) implies cons(ZF + Borel conjecture + there exists a Ramsey ultrafilter). We also prove some results on strong measure zero sets from the existence of generalized Luzin sets. We study the relationships between strong measure zero sets and rapid filters on ω.

Souslin forcing

1988 ◽  
Vol 53 (4) ◽  
pp. 1188-1207 ◽  
Author(s):  
Jaime I. Ihoda ◽  
Saharon Shelah
Keyword(s):  
Inaccessible Cardinal ◽  
Iterated Forcing ◽  
Countable Support ◽  
Martin's Axiom ◽  
Martin’S Axiom ◽  
Splitting Number ◽  
Borel Conjecture

AbstractWe define the notion of Souslin forcing, and we prove that some properties are preserved under iteration. We define a weaker form of Martin's axiom, namely , and using the results on Souslin forcing we show that is consistent with the existence of a Souslin tree and with the splitting number s = ℵ1. We prove that proves the additivity of measure. Also we introduce the notion of proper Souslin forcing, and we prove that this property is preserved under countable support iterated forcing. We use these results to show that ZFC + there is an inaccessible cardinal is equiconsistent with ZFC + the Borel conjecture + -measurability.

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