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