A \({\Delta{}}^ 2_ 2\) well-order of the reals and incompactness of \(L(Q^{MM})\)

DOI10.1016/0168-0072(93)90228-6zbMath0785.03028arXivmath/9812115OpenAlexW2594540614MaRDI QIDQ1208082

Saharon Shelah, Uri Abraham

Publication date: 16 May 1993

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9812115

zbMATH Keywords

productsencodinggeneric extensionAronszajn treesSuslin treesforcing posetdefinable well-order of the realsMagidor-Malitz logic

Mathematics Subject Classification ID

Consistency and independence results (03E35) Logic with extra quantifiers and operators (03C80) Other combinatorial set theory (03E05)

Related Items (16)

Ramsey theory over partitions III: Strongly Luzin sets and partition relations ⋮ Finding generic filters by playing games ⋮ A microscopic approach to Souslin-tree construction. II ⋮ Souslin algebra embeddings ⋮ Inner models from extended logics: Part 1 ⋮ Hedetniemi's conjecture for uncountable graphs ⋮ Terminal notions in set theory ⋮ Coding by club-sequences ⋮ Terminal Notions ⋮ A remark on Schimmerling's question ⋮ Specializing Aronszajn Trees and Preserving Some Weak Diamonds ⋮ Chain homogeneous Souslin algebras ⋮ Incompatible Ω-Complete Theories ⋮ Canonical models for \(\aleph_1\)-combinatorics ⋮ 2005 Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '05 ⋮ Coding with ladders a well ordering of the reals

Cites Work

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• Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable
• Isomorphism types of Aronszajn trees
• Proper forcing
• The Souslin problem
• Large Cardinals from Determinacy
• Compact extensions of L(Q) (part 1a)
• A new construction of non-constructible ${Δ^1}_3$ subset of ω
• Proper and Improper Forcing

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