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