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

• Autorzy: Joan Bagaria , Saharon Shelah
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E50: Continuum hypothesis and Martin's axiom
• 03Exx: Set theory
• 03E57: Generic absoluteness and forcing axioms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 232
• Numer: 2
• Strony: 181-197

Daty

wydano

2016

Twórcy

autor

Joan Bagaria

• ICREA (Institució Catalana de Recerca, i Estudis Avançats)
• Departament de Lògica, Història, i Filosofia de la Ciència, Universitat de Barcelona, Montalegre 6, 08001 Barcelona, Catalonia, Spain

autor

Saharon Shelah

• Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel

Identyfikatory

DOI

10.4064/fm232-2-6