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Successor of Regular Cardinal Diamond-sharp Ascending path Iterated forcing b-scale xbox Antichain Club Guessing Hereditarily Lindelöf space strongly bounded groups nonmeager set SNR stationary hitting Almost Souslin Successor of Singular Cardinal Foundations L-space Cardinal Invariants Strong coloring Dushnik-Miller Subadditive Diamond for trees polarized partition relation Constructible Universe GMA Almost-disjoint family Mandelbrot set reflection principles Jonsson cardinal Absoluteness tensor product graph Intersection model Prevalent singular cardinals Parameterized proxy principle Sierpinski's onto mapping principle HOD Poset Partition relations for trees Closed coloring C-sequence free Souslin tree Entangled linear order Analytic sets Diamond Martin's Axiom Local Club Condensation. Nonspecial tree Selective Ultrafilter Small forcing Ascent Path coloring number higher Baire space Was Ulam right? super-Souslin tree Strongly compact cardinal Erdos Cardinal projective Boolean algebra Uniformization Monotonically far perfectly normal Uniformly homogeneous Square-Brackets Partition Relations Shelah's Strong Hypothesis Open Access Fat stationary set Vanishing levels Strongly Luzin set club_AD Commutative projection system Whitehead Problem diamond star Rainbow sets Filter reflection Coherent tree Singular Density Amenable C-sequence countably metacompact square principles stick transformations weak Kurepa tree incompactness S-Space Reduced Power Aronszajn tree Kurepa Hypothesis ZFC construction Ineffable cardinal Singular cofinality positive partition relation Hedetniemi's conjecture approachability ideal Reflecting stationary set ccc Ostaszewski square Cohen real Postprocessing function regressive Souslin tree middle diamond Dowker space Souslin Tree Greatly Mahlo Universal Sequences Cardinal function Rado's conjecture Luzin set Respecting tree Slim tree Erdos-Hajnal graphs full tree Almost countably chromatic Rock n' Roll Chang's conjecture Knaster Well-behaved magma PFA(S)[S] Partition Relations Subtle cardinal P-Ideal Dichotomy Minimal Walks Singular cardinals combinatorics Large Cardinals Lipschitz reduction Forcing with side conditions OCA Forcing Forcing Axioms square Distributive tree Prikry-type forcing AIM forcing Subtle tree property Chromatic number unbounded function Fodor-type reflection Non-saturation Generalized descriptive set theory Microscopic Approach Ulam matrix very good scale weak diamond Interval topology on trees Countryman line indecomposable filter stationary reflection Ramsey theory over partitions Uniformly coherent free Boolean algebra Precaliber specializable Souslin tree weak square Commutative cancellative semigroups Sakurai's Bell inequality PFA Knaster and friends Weakly compact cardinal Generalized Clubs Hindman's Theorem O-space Subnormal ideal Fast club 54G20 Axiom R Sigma-Prikry sap
Tag Archives: Souslin Tree
A new model for all C-sequences are trivial
Joint work with Zhixing You and Jiachen Yuan. Abstract. We construct a model in which all C-sequences are trivial, yet there exists a $\kappa$-Souslin tree with full vanishing levels. This answers a question from a previous paper, and provides an … Continue reading
Posted in Compactness, Publications
Tagged Ascent Path, C-sequence, Intersection model, Souslin Tree, Subtle tree property, Vanishing levels
2 Comments
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
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
1 Comment
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
1 Comment
6th European Set Theory Conference, July 2017
I gave a 3-lecture tutorial at the 6th European Set Theory Conference in Budapest, July 2017. Title: Strong colorings and their applications. Abstract. Consider the following questions. Is the product of two $\kappa$-cc partial orders again $\kappa$-cc? Does there exist … Continue reading
Posted in Invited Talks, Open Problems
Tagged b-scale, Cohen real, Luzin set, Minimal Walks, Souslin Tree, Square-Brackets Partition Relations
4 Comments
ASL North American Meeting, March 2017
I gave a plenary talk at the 2017 ASL North American Meeting in Boise, March 2017. Talk Title: The current state of the Souslin problem. Abstract: Recall that the real line is that unique separable, dense linear ordering with no endpoints in … Continue reading
Set Theory and its Applications in Topology, September 2016
I gave an invited talk at the Set Theory and its Applications in Topology meeting, Oaxaca, September 11-16, 2016. The talk was on the $\aleph_2$-Souslin problem. If you are interested in seeing the effect of a jet lag, the video is … Continue reading
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
