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