On partial orderings having precalibre-ℵ₁ and fragments of Martin's axiom

Joan Bagaria, and Saharon Shelah. "On partial orderings having precalibre-ℵ₁ and fragments of Martin's axiom." Fundamenta Mathematicae 232.2 (2016): 181-197. <http://eudml.org/doc/283100>.

@article{JoanBagaria2016,
abstract = {We define a countable antichain condition (ccc) property for partial orderings, weaker than precalibre-ℵ₁, and show that Martin's axiom restricted to the class of partial orderings that have the property does not imply Martin's axiom for σ-linked partial orderings. This yields a new solution to an old question of the first author about the relative strength of Martin's axiom for σ-centered partial orderings together with the assertion that every Aronszajn tree is special. We also answer a question of J. Steprāns and S. Watson (1988) by showing that, by a forcing that preserves cardinals, one can destroy the precalibre-ℵ₁ property of a partial ordering while preserving its ccc-ness.},
author = {Joan Bagaria, Saharon Shelah},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {2},
pages = {181-197},
title = {On partial orderings having precalibre-ℵ₁ and fragments of Martin's axiom},
url = {http://eudml.org/doc/283100},
volume = {232},
year = {2016},
}

TY - JOUR
AU - Joan Bagaria
AU - Saharon Shelah
TI - On partial orderings having precalibre-ℵ₁ and fragments of Martin's axiom
JO - Fundamenta Mathematicae
PY - 2016
VL - 232
IS - 2
SP - 181
EP - 197
AB - We define a countable antichain condition (ccc) property for partial orderings, weaker than precalibre-ℵ₁, and show that Martin's axiom restricted to the class of partial orderings that have the property does not imply Martin's axiom for σ-linked partial orderings. This yields a new solution to an old question of the first author about the relative strength of Martin's axiom for σ-centered partial orderings together with the assertion that every Aronszajn tree is special. We also answer a question of J. Steprāns and S. Watson (1988) by showing that, by a forcing that preserves cardinals, one can destroy the precalibre-ℵ₁ property of a partial ordering while preserving its ccc-ness.
LA - eng
UR - http://eudml.org/doc/283100
ER -