The bounded proper forcing axiom

DOI10.2307/2275509zbMath0819.03042arXivmath/9501222OpenAlexW2111190351WikidataQ105979012 ScholiaQ105979012MaRDI QIDQ4836043

Saharon Shelah, Martin Goldstern

Publication date: 8 June 1995

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9501222

zbMATH Keywords

consistency strengthregular cardinalbounded proper forcing axiomexistence of a \(\Sigma_ 1\)-reflecting cardinalexistence of isomorphisms between structuresrigidity of a structure

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Models with special properties (saturated, rigid, etc.) (03C50) Set-theoretic model theory (03C55)

Related Items (30)

Distributive proper forcing axiom and cardinal invariants ⋮ Definable MAD families and forcing axioms ⋮ Strongly uplifting cardinals and the boldface resurrection axioms ⋮ Double helix in large large cardinals and iteration of elementary embeddings ⋮ -definability at higher cardinals: Thin sets, almost disjoint families and long well-orders ⋮ Bounded Namba forcing axiom may fail ⋮ Subcomplete forcing principles and definable well‐orders ⋮ Non-absoluteness of Hjorth’s cardinal characterization ⋮ Σ₁(κ)-DEFINABLE SUBSETS OF H(κ⁺) ⋮ Resurrection axioms and uplifting cardinals ⋮ SET MAPPING REFLECTION ⋮ Parametrized Measuring and Club Guessing ⋮ Bounding the consistency strength of a five element linear basis ⋮ HIERARCHIES OF FORCING AXIOMS, THE CONTINUUM HYPOTHESIS AND SQUARE PRINCIPLES ⋮ HIERARCHIES OF (VIRTUAL) RESURRECTION AXIOMS ⋮ Canonical fragments of the strong reflection principle ⋮ Weak diamond and Galvin's property ⋮ Generic absoluteness ⋮ Bounded forcing axioms and the continuum ⋮ What do we need large cardinals for? ⋮ The Tree Property at $\omega _2$ and Bounded Forcing Axioms ⋮ SUBCOMPLETE FORCING, TREES, AND GENERIC ABSOLUTENESS ⋮ The Bounded Axiom A Forcing Axiom ⋮ Proper Forcing, Cardinal Arithmetic, and Uncountable Linear Orders ⋮ Bounded Martin's maximum with an asterisk ⋮ The proper and semi-proper forcing axioms for forcing notions that preserve ℵ₂ or ℵ₃ ⋮ On a convenient property about \([\gamma^{\aleph_0}\)] ⋮ ARONSZAJN TREE PRESERVATION AND BOUNDED FORCING AXIOMS ⋮ COMBINING RESURRECTION AND MAXIMALITY ⋮ Lightface $\Sigma^1_2$-indescribable cardinals

Cites Work

• On potential embedding and versions of Martin's axiom
• Models with second order properties II. Trees with no undefined branches
• Aronszajn trees and the independence of the transfer property
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