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