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