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