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