SET MAPPING REFLECTION

DOI10.1142/S0219061305000407zbMath1082.03042arXivmath/0501526MaRDI QIDQ5694199

Justin Tatch Moore

Publication date: 29 September 2005

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

Full work available at URL: https://arxiv.org/abs/math/0501526

zbMATH Keywords

continuumsquarePFAreflection principleMRPAxiom of ChoiceBPFAProper Forcing Axiomdefinable well ordering

Mathematics Subject Classification ID

Other combinatorial set theory (03E05) Other set-theoretic hypotheses and axioms (03E65) Ordinal and cardinal numbers (03E10) Axiom of choice and related propositions (03E25) Other notions of set-theoretic definability (03E47)

Related Items (39)

Forcing axioms and the continuum hypothesis ⋮ On a class of maximality principles ⋮ Definable MAD families and forcing axioms ⋮ Codings and strongly inaccessible cardinals ⋮ Guessing and non-guessing of canonical functions ⋮ Incompatible bounded category forcing axioms ⋮ A generalization of Martin's axiom ⋮ What makes the continuum ℵ₂ ⋮ KNASTER AND FRIENDS III: SUBADDITIVE COLORINGS ⋮ A direct proof of the five element basis theorem ⋮ Subcomplete forcing principles and definable well‐orders ⋮ Strong Chang's conjecture and the tree property at \(\omega_{2}\) ⋮ On the consistency strength of the proper forcing axiom ⋮ Diagonal reflections on squares ⋮ Coherent sequences and threads ⋮ Parametrized Measuring and Club Guessing ⋮ Definable well-orders of H(ω₂) and GCH ⋮ Bounding the consistency strength of a five element linear basis ⋮ HIERARCHIES OF (VIRTUAL) RESURRECTION AXIOMS ⋮ Almost strong properness ⋮ Martin's maximum and definability in \(H(\aleph_2\)) ⋮ Weak diamond and Galvin's property ⋮ P-ideal dichotomy and weak squares ⋮ The proper forcing axiom, Prikry forcing, and the singular cardinals hypothesis ⋮ Coding by club-sequences ⋮ Martin's maximum\(^{++}\) implies Woodin's axiom \((*)\) ⋮ The Bounded Axiom A Forcing Axiom ⋮ Martin's maximum revisited ⋮ Category forcings, 𝑀𝑀⁺⁺⁺, and generic absoluteness for the theory of strong forcing axioms ⋮ Aronszajn lines and the club filter ⋮ Forcing the mapping reflection principle by finite approximations ⋮ 10th Asian Logic Conference ⋮ The proper forcing axiom and the singular cardinal hypothesis ⋮ BPFA and projective well-orderings of the reals ⋮ MRP, tree properties and square principles ⋮ NS SATURATED AND -DEFINABLE ⋮ DEPENDENT CHOICE, PROPERNESS, AND GENERIC ABSOLUTENESS ⋮ Properness under closed forcing ⋮ Forcing consequences of $PFA$ together with the continuum large

Cites Work

• Martin's maximum, saturated ideals, and nonregular ultrafilters. I
• Partitioning pairs of countable ordinals
• Topics in set theory. Lebesgue measurability, large cardinals, forcing axioms, rho-functions
• Forcing axioms and stationary sets
• Bounded forcing axioms as principles of generic absoluteness
• Generic absoluteness and the continuum
• Iterated Cohen extensions and Souslin's problem
• Square in Core Models
• Forcing Positive Partition Relations
• Partition Problems in Topology
• The bounded proper forcing axiom
• The fine structure of the constructible hierarchy

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