Higher Souslin trees and the GCH, revisited

DOI10.1016/j.aim.2017.03.002zbMath1423.03169OpenAlexW2605361184MaRDI QIDQ2400519

Assaf Rinot

Publication date: 29 August 2017

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2017.03.002

zbMATH Keywords

squareSouslin treeweakly compact cardinalmicroscopic approach

Mathematics Subject Classification ID

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

Related Items

A microscopic approach to Souslin-tree construction. II ⋮ A microscopic approach to Souslin-tree constructions. I. ⋮ Club stationary reflection and the special Aronszajn tree property ⋮ TREES AND STATIONARY REFLECTION AT DOUBLE SUCCESSORS OF REGULAR CARDINALS ⋮ Aronszajn trees, square principles, and stationary reflection ⋮ Souslin trees at successors of regular cardinals ⋮ Reflection principles, GCH and the uniformization properties ⋮ The special Aronszajn tree property ⋮ A Forcing Axiom Deciding the Generalized Souslin Hypothesis ⋮ THE EIGHTFOLD WAY ⋮ On the complexity of classes of uncountable structures: trees on $\aleph _1$ ⋮ A remark on Schimmerling's question ⋮ Transformations of the transfinite plane ⋮ On the ideal \(J[\kappa\)] ⋮ More notions of forcing add a Souslin tree ⋮ A guessing principle from a Souslin tree, with applications to topology

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Splitting families of sets in ZFC
• On guessing generalized clubs at the successors of regulars
• \(\mu\)-complete Souslin trees on \(\mu^ +\)
• A question about Suslin trees and the weak square hierarchy
• Generalized Martin's axiom and Souslin's hypothesis for higher cardinals
• S-forcing. I: a black-box theorem for morasses, with applications to super-Souslin trees
• Some exact equiconsistency results in set theory
• Souslin trees and successors of singular cardinals
• Partitioning pairs of countable ordinals
• Set theory. An introduction to independence proofs
• Proper forcing
• The Souslin problem
• Canonical structure in the universe of set theory. I
• The generalized continuum hypothesis revisited
• The Ostaszewski square and homogeneous Souslin trees
• Iterated Cohen extensions and Souslin's problem
• SQUARES, SCALES AND STATIONARY REFLECTION
• CHAIN CONDITIONS OF PRODUCTS, AND WEAKLY COMPACT CARDINALS
• Jensen's diamond principle and its relatives
• Weakly Compact Cardinals and Nonspecial Aronszajn Trees
• Successors of Singular Cardinals
• Some results on higher Suslin trees
• Reduced powers of $ℵ_2$-trees
• Diamonds
• Combinatorial aspects of measure and category
• Special Square Sequences
• Trees, subtrees and order types
• The ℵ 2 \1-Souslin Hypothesis
• Models with second order properties. III. Omitting types forL(Q)
• A new class of order types
• Almost-disjoint sets the dense set problem and the partition calculus
• Higher Souslin trees and the generalized continuum hypothesis
• A Note on the Combinatorial Principles ◊(E)
• A very weak square principle
• Souslin trees which are hard to specialise
• Reflecting stationary sets
• Advances in Cardinal Arithmetic
• A relative of the approachability ideal, diamond and non-saturation
• Guessing clubs in the generalized club filter
• On SCH and the approachability property
• PFA implies AD^L(ℝ)
• SOUSLIN'S PROBLEM
• Incompactness in languages with infinitely long expressions
• Aronszajn trees and the independence of the transfer property
• The fine structure of the constructible hierarchy
• Sur un problème de Sikorski