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Subtle cardinal Almost countably chromatic Successor of Regular Cardinal L-space Almost Souslin Ramsey theory over partitions Erdos-Hajnal graphs Partition relations for trees Slim tree Prevalent singular cardinals ccc SNR AIM forcing Cardinal function Universal Sequences positive partition relation Vanishing levels Uniformly coherent Amenable C-sequence Erdos Cardinal free Boolean algebra weak square stick indecomposable filter Selective Ultrafilter Minimal Walks Constructible Universe middle diamond Souslin Tree Aronszajn tree Strong coloring GMA Dushnik-Miller Fat stationary set ZFC construction C-sequence incompactness Subtle tree property specializable Souslin tree Foundations Strongly Luzin set Well-behaved magma regressive Souslin tree Successor of Singular Cardinal Axiom R Ostaszewski square Shelah's Strong Hypothesis higher Baire space Whitehead Problem stationary reflection Strongly compact cardinal weak diamond Closed coloring Kurepa Hypothesis Countryman line unbounded function Square-Brackets Partition Relations Singular cardinals combinatorics Non-saturation approachability ideal tensor product graph Was Ulam right? Rock n' Roll Singular Density perfectly normal diamond star club_AD Diamond for trees Commutative projection system square Microscopic Approach Ulam matrix Sakurai's Bell inequality nonmeager set Ascent Path Monotonically far Forcing Axioms Distributive tree strongly bounded groups full tree coloring number Hedetniemi's conjecture Cardinal Invariants square principles Forcing Lipschitz reduction Knaster Absoluteness Subnormal ideal PFA(S)[S] Sigma-Prikry Respecting tree Iterated forcing reflection principles Hindman's Theorem Reduced Power transformations PFA Ascending path Jonsson cardinal Subadditive Rainbow sets Dowker space super-Souslin tree Postprocessing function Uniformly homogeneous Mandelbrot set Filter reflection Analytic sets Partition Relations Uniformization P-Ideal Dichotomy Diamond Nonspecial tree Commutative cancellative semigroups Poset b-scale S-Space 54G20 polarized partition relation Generalized descriptive set theory Club Guessing Small forcing Coherent tree Fast club Intersection model Ineffable cardinal stationary hitting HOD Almost-disjoint family O-space Greatly Mahlo Sierpinski's onto mapping principle Diamond-sharp Open Access OCA Entangled linear order Forcing with side conditions Large Cardinals Fodor-type reflection countably metacompact Antichain Singular cofinality Reflecting stationary set Interval topology on trees free Souslin tree projective Boolean algebra Chromatic number Parameterized proxy principle Hereditarily Lindelöf space Martin's Axiom Chang's conjecture Generalized Clubs xbox Rado's conjecture Knaster and friends Local Club Condensation. Cohen real very good scale Precaliber Prikry-type forcing Luzin set weak Kurepa tree Weakly compact cardinal sap
Tag Archives: Parameterized proxy principle
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 of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. This is an invariant in the … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Almost-disjoint family, Ascent Path, C-sequence, Coherent tree, Dowker space, Open Access, Parameterized proxy principle, regressive Souslin tree, Respecting tree, Subtle tree property, Uniformly homogeneous, Vanishing levels, weak Kurepa tree
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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
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 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
Reflection on the coloring and chromatic numbers
Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Chang's conjecture, Chromatic number, coloring number, Fodor-type reflection, incompactness, Iterated forcing, Parameterized proxy principle, Postprocessing function, Rado's conjecture, square, stationary reflection
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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
A microscopic approach to Souslin-tree constructions. Part I
Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
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