Sh:1041

• Bagaria, J., & Shelah, S. (2016). On partial orderings having precalibre-\aleph_1 and fragments of Martin’s axiom. Fund. Math., 232(2), 181–197. arXiv: 1502.05500 DOI: 10.4064/fm232-2-6 MR: 3418888
• Abstract:
  We define a countable antichain condition (ccc) property for partial orderings, weaker than precalibre-\aleph_1, and show that Martin’s axiom restricted to the class of partial orderings that have the property does not imply Martin’s axiom for \sigma-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 \sigma-centered partial orderings together with the assertion that every Aronszajn tree is special. We also answer a question of J. Steprans and S. Watson (1988) by showing that, by a forcing that preserves cardinals, one can destroy the precalibre-\aleph_1 property of a partial ordering while preserving its ccc-ness.
• Version 2015-06-15_11 (15p) published version (18p)

@article{Sh:1041,
 author = {Bagaria, Joan and Shelah, Saharon},
 title = {{On partial orderings having precalibre-$\aleph_1$ and fragments of Martin's axiom}},
 journal = {Fund. Math.},
 fjournal = {Fundamenta Mathematicae},
 volume = {232},
 number = {2},
 year = {2016},
 pages = {181--197},
 issn = {0016-2736},
 mrnumber = {3418888},
 mrclass = {03E40 (03E35 03E50 03E57)},
 doi = {10.4064/fm232-2-6},
 note = {\href{https://arxiv.org/abs/1502.05500}{arXiv: 1502.05500}},
 arxiv_number = {1502.05500}
}