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