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Interval topology on trees Strongly compact cardinal Partition Relations free Souslin tree Subtle tree property Club Guessing super-Souslin tree Local Club Condensation. Hereditarily Lindelöf space unbounded function projective Boolean algebra Ostaszewski square Well-behaved magma Successor of Regular Cardinal Fodor-type reflection Prikry-type forcing Dowker space free Boolean algebra indecomposable filter Strongly Luzin set Uniformization tensor product graph Parameterized proxy principle AIM forcing Selective Ultrafilter Knaster Sigma-Prikry PFA Almost countably chromatic very good scale Closed coloring HOD Strong coloring Poset Sierpinski's onto mapping principle stick SNR weak Kurepa tree Martin's Axiom Respecting tree stationary hitting Generalized descriptive set theory Sakurai's Bell inequality Subtle cardinal OCA Singular cardinals combinatorics Luzin set Open Access countably metacompact sap P-Ideal Dichotomy strongly bounded groups Ramsey theory over partitions Reflecting stationary set middle diamond Filter reflection perfectly normal Prevalent singular cardinals Vanishing levels Chromatic number Forcing Axioms ccc Non-saturation Uniformly coherent full tree approachability ideal L-space incompactness Ascending path club_AD Distributive tree Square-Brackets Partition Relations weak diamond Entangled linear order Ulam matrix Aronszajn tree Partition relations for trees positive partition relation Coherent tree xbox transformations Rado's conjecture Intersection model Jonsson cardinal ZFC construction higher Baire space Precaliber Was Ulam right? Countryman line Cardinal function Singular Density Small forcing Iterated forcing Cardinal Invariants Ineffable cardinal Greatly Mahlo Cohen real GMA Hindman's Theorem S-Space Nonspecial tree Hedetniemi's conjecture diamond star reflection principles Forcing PFA(S)[S] Erdos Cardinal Foundations Microscopic Approach Weakly compact cardinal Monotonically far Chang's conjecture Forcing with side conditions Subadditive Diamond Almost-disjoint family stationary reflection Dushnik-Miller Whitehead Problem Almost Souslin b-scale Successor of Singular Cardinal polarized partition relation Reduced Power square principles Shelah's Strong Hypothesis Axiom R nonmeager set regressive Souslin tree Erdos-Hajnal graphs Generalized Clubs Fast club Subnormal ideal Minimal Walks Rainbow sets Kurepa Hypothesis Absoluteness specializable Souslin tree Analytic sets Singular cofinality Diamond-sharp Slim tree 54G20 Rock n' Roll Antichain weak square Large Cardinals square Fat stationary set O-space Amenable C-sequence Souslin Tree Mandelbrot set Knaster and friends Commutative projection system Ascent Path Universal Sequences Diamond for trees Constructible Universe C-sequence Commutative cancellative semigroups Postprocessing function Lipschitz reduction coloring number Uniformly homogeneous
Tag Archives: Souslin Tree
More notions of forcing add a square
Joint work with Yair Hayut and Zhixing You. Abstract. Foreman and Magidor showed that the continuum hypothesis implies the existence of a countably-closed $\aleph_2$-cc forcing notion $\mathbb P$ for adding $\square_{\omega_1}$. Here, we show that $\mathbb P$ may consistently be … Continue reading
Posted in Squares and Diamonds
Tagged full tree, Souslin Tree, square principles, super-Souslin tree
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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
