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