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indecomposable filter Fat stationary set Mandelbrot set Coherent tree free Boolean algebra specializable Souslin tree countably metacompact Universal Sequences b-scale Countryman line Distributive tree Slim tree GMA Entangled linear order Constructible Universe Reflecting stationary set Partition relations for trees reflection principles Uniformization Greatly Mahlo weak square Chromatic number Almost-disjoint family Dowker space xbox square Forcing Almost Souslin strongly bounded groups Selective Ultrafilter Local Club Condensation. Cohen real Singular cardinals combinatorics regressive Souslin tree Open Access Erdos Cardinal transformations Generalized descriptive set theory Commutative projection system unbounded function Forcing with side conditions Partition Relations Erdos-Hajnal graphs Subnormal ideal Shelah's Strong Hypothesis Square-Brackets Partition Relations O-space Ascent Path Sakurai's Bell inequality Luzin set coloring number stick Rock n' Roll P-Ideal Dichotomy Knaster and friends Cardinal Invariants OCA Reduced Power Prevalent singular cardinals Was Ulam right? Prikry-type forcing Nonspecial tree PFA(S)[S] Weakly compact cardinal polarized partition relation L-space Intersection model Forcing Axioms diamond star Filter reflection ccc ZFC construction Club Guessing Parameterized proxy principle Subtle cardinal Generalized Clubs Hindman's Theorem Interval topology on trees Lipschitz reduction Successor of Regular Cardinal Knaster Absoluteness very good scale Almost countably chromatic Sierpinski's onto mapping principle Strongly Luzin set PFA nonmeager set tensor product graph Singular Density weak Kurepa tree Analytic sets super-Souslin tree Uniformly coherent Commutative cancellative semigroups Postprocessing function Dushnik-Miller full tree Uniformly homogeneous weak diamond Strong coloring Successor of Singular Cardinal Hereditarily Lindelöf space AIM forcing Singular cofinality approachability ideal Rado's conjecture Axiom R Rainbow sets Monotonically far perfectly normal Foundations projective Boolean algebra stationary reflection Ramsey theory over partitions Kurepa Hypothesis Amenable C-sequence incompactness Respecting tree middle diamond Whitehead Problem Cardinal function Diamond for trees Closed coloring free Souslin tree positive partition relation Hedetniemi's conjecture Minimal Walks Ineffable cardinal HOD C-sequence square principles Poset Iterated forcing Chang's conjecture Diamond-sharp Fodor-type reflection Diamond Fast club stationary hitting higher Baire space Precaliber Vanishing levels Well-behaved magma SNR Martin's Axiom Small forcing Subadditive Large Cardinals Subtle tree property Strongly compact cardinal sap Jonsson cardinal Ostaszewski square club_AD Non-saturation Ulam matrix Ascending path Sigma-Prikry Microscopic Approach Souslin Tree Aronszajn tree Antichain 54G20 S-Space
Category Archives: Souslin Hypothesis
Higher Souslin trees and the GCH, revisited
Abstract. It is proved that for every uncountable cardinal $\lambda$, GCH+$\square(\lambda^+)$ entails the existence of a $\text{cf}(\lambda)$-complete $\lambda^+$-Souslin tree. In particular, if GCH holds and there are no $\aleph_2$-Souslin trees, then $\aleph_2$ is weakly compact in Godel’s constructible universe, improving … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, Open Access, regressive Souslin tree, Souslin Tree, square, Weakly compact cardinal, xbox
16 Comments
A microscopic approach to Souslin-tree constructions. Part I
Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
5 Comments
Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading
On guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading
The Ostaszewski square, and homogeneous Souslin trees
Abstract: Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $\left\langle C_\alpha \mid \alpha<\lambda^+\right\rangle$ with the following remarkable guessing property: For every sequence $\langle A_i\mid i<\lambda\rangle$ … Continue reading
Posted in Publications, Souslin Hypothesis, Squares and Diamonds
Tagged 03E05, 03E35, Club Guessing, Fat stationary set, Ostaszewski square, Souslin Tree
5 Comments
