Archives
Keywords
Foundations Ineffable cardinal Strongly Luzin set Precaliber Fodor-type reflection specializable Souslin tree Rock n' Roll approachability ideal free Boolean algebra S-Space Whitehead Problem weak diamond Amenable C-sequence Antichain Singular Density Sigma-Prikry Subtle tree property 54G20 incompactness PFA Knaster square Hindman's Theorem Mandelbrot set Lipschitz reduction Ostaszewski square Generalized descriptive set theory PFA(S)[S] Shelah's Strong Hypothesis Dowker space Cardinal Invariants Generalized Clubs Martin's Axiom stick free Souslin tree ccc club_AD Was Ulam right P-Ideal Dichotomy Subnormal ideal Prikry-type forcing SNR weak square Strongly compact cardinal Partition Relations higher Baire space Reflecting stationary set xbox C-sequence Dushnik-Miller Axiom R Slim tree Parameterized proxy principle Hereditarily Lindelöf space Square-Brackets Partition Relations Club Guessing Diamond Open Access Iterated forcing countably metacompact Cardinal function Large Cardinals Successor of Singular Cardinal b-scale Well-behaved magma Sakurai's Bell inequality Souslin Tree tensor product graph Ulam matrix Diamond for trees Fast club AIM forcing projective Boolean algebra Successor of Regular Cardinal Erdos-Hajnal graphs nonmeager set Uniformly coherent Kurepa Hypothesis Weakly compact cardinal Rado's conjecture Almost countably chromatic Subtle cardinal square principles Uniformization Cohen real Greatly Mahlo Knaster and friends weak Kurepa tree Prevalent singular cardinals indecomposable ultrafilter super-Souslin tree Selective Ultrafilter Local Club Condensation. Universal Sequences polarized partition relation middle diamond Commutative projection system Countryman line Closed coloring Commutative cancellative semigroups Ramsey theory over partitions Diamond-sharp positive partition relation unbounded function Singular cardinals combinatorics Almost-disjoint family Vanishing levels Subadditive stationary reflection Minimal Walks Intersection model transformations reflection principles Fat stationary set Almost Souslin Small forcing Reduced Power Coherent tree Luzin set stationary hitting Nonspecial tree Strong coloring GMA Jonsson cardinal Chang's conjecture Non-saturation OCA HOD strongly bounded groups Forcing Axioms Respecting tree Singular cofinality Forcing Rainbow sets very good scale Constructible Universe Sierpinski's onto mapping principle diamond star Analytic sets Aronszajn tree ZFC construction coloring number Postprocessing function Poset Absoluteness Erdos Cardinal Chromatic number regressive Souslin tree Ascent Path Filter reflection Uniformly homogeneous Microscopic Approach full tree O-space sap Distributive tree Hedetniemi's conjecture L-space
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 $\kappa$-Souslin trees in a uniform way that does not … Continue reading
The vanishing levels of a tree
Joint work with Shira Yadai and Zhixing You. Abstract. We initiate the study of the spectrum $Vspec(\kappa)$ of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. The latter is an invariant in … Continue reading
Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
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 $J[\kappa]$, from which we confirm that $\kappa$-Souslin trees exist in various models of interest. As a corollary we … Continue reading
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 $\clubsuit_{AD}$. 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 remark on Schimmerling’s question
Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading
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
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
