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Rado's conjecture Ineffable cardinal Poset Commutative projection system Successor of Singular Cardinal Vanishing levels stationary hitting transformations specializable Souslin tree Local Club Condensation. Universal Sequences Whitehead Problem square Aronszajn tree Filter reflection Weakly compact cardinal positive partition relation Generalized Clubs Absoluteness Prikry-type forcing Kurepa Hypothesis Erdos Cardinal Fat stationary set Antichain Diamond for trees b-scale S-Space perfectly normal Fodor-type reflection Strong coloring Was Ulam right? Strongly compact cardinal diamond star PFA Subtle tree property Ascending path super-Souslin tree free Boolean algebra L-space square principles stick Forcing Axioms Hindman's Theorem Reflecting stationary set nonmeager set Precaliber Entangled linear order Chang's conjecture Knaster and friends Open Access Ramsey theory over partitions Small forcing Chromatic number Rock n' Roll Ascent Path Forcing Diamond coloring number Successor of Regular Cardinal Uniformly coherent O-space weak Kurepa tree Constructible Universe 54G20 xbox Iterated forcing Respecting tree Almost countably chromatic Foundations Shelah's Strong Hypothesis Axiom R Fast club Hedetniemi's conjecture Large Cardinals Cohen real very good scale HOD Forcing with side conditions unbounded function Uniformization ccc Martin's Axiom Sigma-Prikry Microscopic Approach Well-behaved magma Strongly Luzin set incompactness Generalized descriptive set theory middle diamond approachability ideal Rainbow sets club_AD Knaster strongly bounded groups Interval topology on trees Dowker space polarized partition relation Intersection model Hereditarily Lindelöf space Minimal Walks Commutative cancellative semigroups full tree Diamond-sharp C-sequence P-Ideal Dichotomy Prevalent singular cardinals Non-saturation SNR regressive Souslin tree AIM forcing ZFC construction Dushnik-Miller Subtle cardinal Singular cardinals combinatorics Singular cofinality PFA(S)[S] Nonspecial tree Sakurai's Bell inequality Singular Density Postprocessing function weak square Ulam matrix Partition Relations Analytic sets Slim tree Closed coloring indecomposable filter Cardinal function Distributive tree Cardinal Invariants Amenable C-sequence Subnormal ideal higher Baire space Almost Souslin weak diamond Sierpinski's onto mapping principle OCA Mandelbrot set projective Boolean algebra sap Selective Ultrafilter Ostaszewski square Lipschitz reduction Jonsson cardinal reflection principles tensor product graph Reduced Power Parameterized proxy principle Luzin set free Souslin tree Countryman line Greatly Mahlo Subadditive Almost-disjoint family Uniformly homogeneous Monotonically far countably metacompact Partition relations for trees Club Guessing Square-Brackets Partition Relations stationary reflection Erdos-Hajnal graphs Coherent tree Souslin Tree GMA
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
