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