Proper Forcing, Cardinal Arithmetic, and Uncountable Linear Orders

DOI10.2178/bsl/1107959499zbMath1095.03054OpenAlexW2141464214MaRDI QIDQ3370627

Justin Tatch Moore

Publication date: 8 February 2006

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

Full work available at URL: https://doi.org/10.2178/bsl/1107959499

zbMATH Keywords

uncountable linear ordersCountryman lineBounded Proper Forcing Axiomconsequences of the Proper Forcing AxiomSingular Cardinals Hypothesiswell-ordering of the reals

Mathematics Subject Classification ID

Other combinatorial set theory (03E05) Other set-theoretic hypotheses and axioms (03E65) Partition relations (03E02) Other aspects of forcing and Boolean-valued models (03E40)

Related Items (2)

What do we need large cardinals for? ⋮ The Tree Property at $\omega _2$ and Bounded Forcing Axioms

Cites Work

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• Isomorphism types of Aronszajn trees
• On the consistency of some partition theorems for continuous colorings, and the structure of \(\aleph _ 1\)-dense real order types
• Martin's maximum, saturated ideals, and nonregular ultrafilters. I
• Partitioning pairs of countable ordinals
• Forcing axioms and stationary sets
• Decomposing uncountable squares to countably many chains
• Bounded forcing axioms as principles of generic absoluteness
• Indexed squares
• Generic absoluteness and the continuum
• Partition Problems in Topology
• Projective Stationary Sets and a Strong Reflection Principle
• The bounded proper forcing axiom

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