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Uniformly homogeneous Entangled linear order O-space Chromatic number 54G20 Ineffable cardinal Reduced Power full tree Antichain Chang's conjecture Luzin set indecomposable filter incompactness Sierpinski's onto mapping principle Prevalent singular cardinals weak diamond Subadditive Non-saturation GMA Hedetniemi's conjecture countably metacompact polarized partition relation S-Space Diamond-sharp Ascending path Commutative projection system projective Boolean algebra stick Small forcing Ostaszewski square unbounded function Subtle tree property Postprocessing function Universal Sequences tensor product graph P-Ideal Dichotomy Kurepa Hypothesis perfectly normal Mandelbrot set Distributive tree Aronszajn tree Club Guessing weak Kurepa tree Coherent tree Martin's Axiom Successor of Regular Cardinal Intersection model Ulam matrix Diamond for trees Respecting tree PFA(S)[S] Generalized Clubs Strongly compact cardinal Partition Relations Shelah's Strong Hypothesis OCA Cardinal Invariants higher Baire space Amenable C-sequence Strong coloring very good scale xbox SNR club_AD Jonsson cardinal Uniformization Uniformly coherent middle diamond Singular Density free Souslin tree HOD C-sequence specializable Souslin tree Rock n' Roll Dowker space Sigma-Prikry square reflection principles Almost Souslin b-scale Successor of Singular Cardinal Well-behaved magma Ramsey theory over partitions Forcing with side conditions Rainbow sets Microscopic Approach Constructible Universe weak square Fodor-type reflection Souslin Tree Closed coloring Cardinal function Fast club Erdos Cardinal sap Hindman's Theorem Countryman line Subtle cardinal Diamond Almost countably chromatic Iterated forcing Foundations Rado's conjecture Partition relations for trees Nonspecial tree Greatly Mahlo Generalized descriptive set theory PFA Dushnik-Miller Subnormal ideal Lipschitz reduction stationary reflection Whitehead Problem Absoluteness Selective Ultrafilter Vanishing levels Knaster Precaliber Analytic sets Open Access AIM forcing Weakly compact cardinal transformations Was Ulam right? Singular cardinals combinatorics ZFC construction Square-Brackets Partition Relations Interval topology on trees Poset stationary hitting ccc regressive Souslin tree Knaster and friends strongly bounded groups Prikry-type forcing Parameterized proxy principle nonmeager set Minimal Walks Local Club Condensation. Erdos-Hajnal graphs free Boolean algebra Strongly Luzin set Large Cardinals Slim tree Forcing Forcing Axioms super-Souslin tree square principles Axiom R Reflecting stationary set Singular cofinality Commutative cancellative semigroups L-space Hereditarily Lindelöf space Fat stationary set Filter reflection Sakurai's Bell inequality Ascent Path Almost-disjoint family Cohen real Monotonically far approachability ideal diamond star coloring number positive partition relation
Category Archives: Souslin Hypothesis
Proxy principles in combinatorial set theory
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper as new foundations for the construction of $\kappa$-Souslin trees in a uniform way that does not … Continue reading
The vanishing levels of a tree
Joint work with Shira Yadai and Zhixing You. Abstract. We initiate the study of the spectrum of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. This is an invariant in the … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Almost-disjoint family, Ascent Path, C-sequence, Coherent tree, Dowker space, Open Access, Parameterized proxy principle, regressive Souslin tree, Respecting tree, Subtle tree property, Uniformly homogeneous, Vanishing levels, weak Kurepa tree
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Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
On the ideal J[kappa]
Abstract. Motivated by a question from a recent paper by Gilton, Levine and Stejskalova, we obtain a new characterization of the ideal $J[\kappa]$, from which we confirm that $\kappa$-Souslin trees exist in various models of interest. As a corollary we … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged Cardinal Invariants, Cohen real, nonmeager set
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A microscopic approach to Souslin-tree constructions. Part II
Joint work with Ari Meir Brodsky. Abstract. In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known $\diamondsuit$-based constructions of Souslin trees with various additional properties may be rendered as applications of … Continue reading
Souslin trees at successors of regular cardinals
Abstract. We present a weak sufficient condition for the existence of Souslin trees at successor of regular cardinals. The result is optimal and simultaneously improves an old theorem of Gregory and a more recent theorem of the author. Downloads: Citation … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged Parameterized proxy principle, Souslin Tree
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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 forcing axiom deciding the generalized Souslin Hypothesis
Joint work with Chris Lambie-Hanson. Abstract. We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal $\lambda$, … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, Souslin Tree, square, super-Souslin tree
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More notions of forcing add a Souslin tree
Joint work with Ari Meir Brodsky. Abstract. An $\aleph_1$-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech devised notions of forcing for introducing … Continue reading
