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