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