Generic Vopěnka's principle, remarkable cardinals, and the weak proper forcing axiom

DOI10.1007/s00153-016-0511-xzbMath1417.03260OpenAlexW2528948859WikidataQ114018311 ScholiaQ114018311MaRDI QIDQ512131

Victoria Gitman, Joan Bagaria, Ralf-Dieter Schindler

Publication date: 24 February 2017

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00153-016-0511-x

zbMATH Keywords

large cardinalsproper forcing axiomgeneric Vopěnka's principleremarkable cardinalsVopěnka's principle

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Generic absoluteness and forcing axioms (03E57)

Related Items (12)

LARGE CARDINALS AS PRINCIPLES OF STRUCTURAL REFLECTION ⋮ THE CONSISTENCY STRENGTH OF THE PERFECT SET PROPERTY FOR UNIVERSALLY BAIRE SETS OF REALS ⋮ Structural reflection, shrewd cardinals and the size of the continuum ⋮ A model of the generic Vopěnka principle in which the ordinals are not Mahlo ⋮ MODELS OF POSITIVE TRUTH ⋮ HIERARCHIES OF FORCING AXIOMS, THE CONTINUUM HYPOTHESIS AND SQUARE PRINCIPLES ⋮ HIERARCHIES OF (VIRTUAL) RESURRECTION AXIOMS ⋮ Generic Vopěnka cardinals and models of ZF with few \(\aleph _1\)-Suslin sets ⋮ WEAKLY REMARKABLE CARDINALS, ERDŐS CARDINALS, AND THE GENERIC VOPĚNKA PRINCIPLE ⋮ Virtual large cardinals ⋮ ARONSZAJN TREE PRESERVATION AND BOUNDED FORCING AXIOMS ⋮ MORE ON THE PRESERVATION OF LARGE CARDINALS UNDER CLASS FORCING

Cites Work

• \(C ^{(n)}\)-cardinals
• Indestructibility properties of remarkable cardinals
• Virtual large cardinals
• Set theory. Exploring independence and truth
• On the role of supercompact and extendible cardinals in logic
• Woodin's axiom (*), bounded forcing axioms, and precipitous ideals on ω₁
• Ramsey-like cardinals II
• Elementary embeddings and infinitary combinatorics
• Proper Forcing and Remarkable Cardinals
• HARRINGTON’S PRINCIPLE IN HIGHER ORDER ARITHMETIC
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Generic Vopěnka's principle, remarkable cardinals, and the weak proper forcing axiom