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