SUBCOMPLETE FORCING, TREES, AND GENERIC ABSOLUTENESS

DOI10.1017/jsl.2018.23zbMath1502.03013arXiv1708.08170OpenAlexW2962812905WikidataQ129037858 ScholiaQ129037858MaRDI QIDQ4692091

Kaethe Minden, Gunter Fuchs

Publication date: 26 October 2018

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

Full work available at URL: https://arxiv.org/abs/1708.08170

zbMATH Keywords

continuum hypothesisforcing axiomsgeneric absolutenessSuslin treessubcomplete forcing

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Continuum hypothesis and Martin's axiom (03E50) Other combinatorial set theory (03E05) Generic absoluteness and forcing axioms (03E57)

Related Items (9)

Subcomplete forcing principles and definable well‐orders ⋮ The special tree number ⋮ Forcing axioms via ground model interpretations ⋮ Diagonal reflections on squares ⋮ HIERARCHIES OF (VIRTUAL) RESURRECTION AXIOMS ⋮ Closure properties of parametric subcompleteness ⋮ The subcompleteness of diagonal Prikry ⋮ ARONSZAJN TREE PRESERVATION AND BOUNDED FORCING AXIOMS ⋮ COMBINING RESURRECTION AND MAXIMALITY

Cites Work

• Bounded forcing axioms as principles of generic absoluteness
• Weak square and stationary reflection
• Closure properties of parametric subcompleteness
• Specializing Aronszajn Trees and Preserving Some Weak Diamonds
• SUBCOMPLETE FORCING AND ℒ-FORCING
• Degrees of rigidity for Souslin trees
• On Closed Sets of Ordinals
• HIERARCHIES OF FORCING AXIOMS, THE CONTINUUM HYPOTHESIS AND SQUARE PRINCIPLES
• HIERARCHIES OF (VIRTUAL) RESURRECTION AXIOMS
• The bounded proper forcing axiom
• Closed maximality principles: implications, separations and combinations

This page was built for publication: SUBCOMPLETE FORCING, TREES, AND GENERIC ABSOLUTENESS