Authors: Guzmán, Osvaldo
Todorčević, Stevo 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: The P-ideal dichotomy, Martin’s axiom and entangled sets
Journal: Israel Journal of Mathematics
Issue Date: 2024
Rank: ~M22
ISSN: 0021-2172
DOI: 10.1007/s11856-024-2651-8
Abstract: 
We build a model of the P-ideal ichotomy (PID) and Martin’s axiom for ω1 (MAω1) in which there is a 2-entangled set of reals. In particular, it follows that the Open Graph Axiom or Baumgartner’s axiom for ω1-dense sets are not consequences of PID+MAω1. We review Neeman’s iteration method using two type side conditions and provide an alternative proof for the preservation of properness.
Publisher: Springer Link

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