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Postprocessing function O-space GMA S-Space specializable Souslin tree SNR Uniformly homogeneous Rado's conjecture Diamond-sharp Baumgartner's square Sigma-Prikry Uniformization Diamond for trees higher Baire space Hedetniemi's conjecture countably metacompact Hereditarily Lindelöf space regressive Souslin tree club_AD Forcing perfectly normal Jonsson cardinal Knaster and friends Countryman line stationary hitting transformations Forcing Axioms Shelah's Strong Hypothesis Prevalent singular cardinals Hindman's Theorem Respecting tree middle diamond Sakurai's Bell inequality Reflecting stationary set Small forcing Ulam matrix Large Cardinals Rock n' Roll square Open Access Microscopic Approach Interval topology on trees Subtle cardinal Club Guessing Cardinal function Analytic sets Almost-disjoint family nonmeager set stick polarized partition relation Partition Relations Dushnik-Miller weak square full tree Axiom R reflection principles Filter reflection Nonspecial tree Mandelbrot set positive partition relation Erdos-Hajnal graphs Selective Ultrafilter Non-saturation PFA L-space Sierpinski's onto mapping principle Martin's Axiom b-scale Aronszajn tree Luzin set Was Ulam right? Foundations Generalized Clubs Weakly compact cardinal free Souslin tree weak diamond Diamond projective Boolean algebra Antichain Generalized descriptive set theory HOD ZFC construction Square-Brackets Partition Relations Strongly compact cardinal P-Ideal Dichotomy weak Kurepa tree Poset Minimal Walks Almost Souslin Ostaszewski square Universal Sequences Well-behaved magma PFA(S)[S] square principles Fast club Kurepa Hypothesis AIM forcing incompactness Dowker space Erdos Cardinal Successor of Singular Cardinal very good scale Souslin Tree Subadditive super-Souslin tree Subtle tree property 54G20 coloring number C-sequence Strong coloring Rainbow sets ccc indecomposable filter approachability ideal Entangled linear order Prikry-type forcing Uniformly coherent Cardinal Invariants Singular cofinality Fodor-type reflection Intersection model sap tensor product graph Commutative cancellative semigroups Chromatic number Partition relations for trees OCA Distributive tree Precaliber Almost countably chromatic diamond star Ineffable cardinal Absoluteness Greatly Mahlo Subnormal ideal Ascending path Strongly Luzin set Lipschitz reduction Singular Density Local Club Condensation. Whitehead Problem Singular cardinals combinatorics Cohen real Amenable C-sequence Chang's conjecture free Boolean algebra Parameterized proxy principle Constructible Universe Ramsey theory over partitions stationary reflection Ascent Path Knaster Fat stationary set Slim tree strongly bounded groups Forcing with side conditions unbounded function Successor of Regular Cardinal Monotonically far Reduced Power Iterated forcing Coherent tree Commutative projection system xbox Vanishing levels Closed coloring
Tag Archives: 05C05
A remark on Schimmerling’s question
Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading
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
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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
