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Nonspecial tree Almost countably chromatic Analytic sets Forcing Axioms Strong coloring approachability ideal Kurepa Hypothesis stationary hitting Poset Subnormal ideal Uniformly coherent higher Baire space Was Ulam right Rainbow sets AIM forcing PFA Amenable C-sequence Generalized Clubs Parameterized proxy principle Knaster regressive Souslin tree Iterated forcing b-scale Dushnik-Miller Coherent tree Whitehead Problem Slim tree Erdos Cardinal ZFC construction Almost Souslin Selective Ultrafilter xbox Constructible Universe Antichain sap strongly bounded groups Cohen real P-Ideal Dichotomy Cardinal Invariants Non-saturation Sierpinski's onto mapping principle unbounded function Hereditarily Lindelöf space Successor of Regular Cardinal Diamond-sharp Absoluteness Filter reflection Martin's Axiom Uniformly homogeneous Sigma-Prikry countably metacompact O-space GMA L-space Minimal Walks transformations indecomposable ultrafilter Prevalent singular cardinals Subadditive Forcing Singular cardinals combinatorics Aronszajn tree Large Cardinals Strongly Luzin set Fat stationary set Rado's conjecture club_AD Dowker space tensor product graph Singular cofinality Postprocessing function OCA Universal Sequences Commutative cancellative semigroups Axiom R Foundations square principles Successor of Singular Cardinal Diamond for trees Rock n' Roll Hedetniemi's conjecture S-Space Partition Relations super-Souslin tree Ascent Path Chang's conjecture C-sequence HOD Reduced Power Open Access very good scale Ulam matrix Chromatic number Distributive tree Fodor-type reflection Shelah's Strong Hypothesis free Boolean algebra Diamond ccc Weakly compact cardinal Fast club 54G20 free Souslin tree stick Almost-disjoint family Small forcing Mandelbrot set Well-behaved magma Ostaszewski square Greatly Mahlo Cardinal function Reflecting stationary set Prikry-type forcing nonmeager set Subtle tree property Singular Density Souslin Tree Precaliber square stationary reflection incompactness PFA(S)[S] SNR reflection principles Generalized descriptive set theory Subtle cardinal specializable Souslin tree Luzin set Vanishing levels Lipschitz reduction polarized partition relation Uniformization positive partition relation Ramsey theory over partitions coloring number weak diamond Ineffable cardinal Local Club Condensation. projective Boolean algebra Erdos-Hajnal graphs Jonsson cardinal diamond star Microscopic Approach Hindman's Theorem Closed coloring middle diamond full tree Square-Brackets Partition Relations Knaster and friends Club Guessing Sakurai's Bell inequality weak square
Tag Archives: Souslin Tree
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
Posted in Preprints, Souslin Hypothesis
Tagged C-sequence, free Souslin tree, Parameterized proxy principle, Souslin Tree, specializable Souslin tree, square principles, xbox
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A guessing principle from a Souslin tree, with applications to topology
Joint work with Roy Shalev. Abstract. We introduce a new combinatorial principle which we call $\clubsuit_{AD}$. This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointness features, and is shown to be sufficient for carrying out … Continue reading
Posted in Publications, Souslin Hypothesis, Topology
Tagged club_AD, Dowker space, O-space, regressive Souslin tree, S-Space, Souslin Tree, Vanishing levels
2 Comments
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
Prikry forcing may add a Souslin tree
A celebrated theorem of Shelah states that adding a Cohen real introduces a Souslin tree. Are there any other examples of notions of forcing that add a $\kappa$-Souslin tree? and why is this of interest? My motivation comes from a … Continue reading