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