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