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C-sequence Club Guessing stick Local Club Condensation. weak diamond Amenable C-sequence Strongly compact cardinal 54G20 polarized partition relation free Souslin tree middle diamond AIM forcing Foundations Lipschitz reduction Almost Souslin Sakurai's Bell inequality Closed coloring Precaliber Iterated forcing S-Space Coherent tree Diamond for trees strongly bounded groups Fodor-type reflection Ramsey theory over partitions Forcing with side conditions Erdos-Hajnal graphs Cohen real b-scale Hedetniemi's conjecture Successor of Regular Cardinal Reflecting stationary set Luzin set xbox Commutative projection system Dowker space Microscopic Approach Slim tree PFA(S)[S] very good scale Jonsson cardinal Shelah's Strong Hypothesis Singular Density Large Cardinals Forcing Axioms Cardinal Invariants square principles stationary hitting Partition relations for trees Fat stationary set Diamond O-space Subnormal ideal Ascent Path Open Access Entangled linear order ZFC construction Partition Relations GMA reflection principles Countryman line approachability ideal Minimal Walks free Boolean algebra Intersection model OCA HOD unbounded function Prevalent singular cardinals Generalized descriptive set theory Selective Ultrafilter Square-Brackets Partition Relations countably metacompact club_AD positive partition relation Mandelbrot set PFA Rock n' Roll Greatly Mahlo Dushnik-Miller Sierpinski's onto mapping principle Axiom R Interval topology on trees indecomposable filter sap Fast club Strongly Luzin set Aronszajn tree Kurepa Hypothesis Non-saturation Vanishing levels Parameterized proxy principle Ineffable cardinal Singular cofinality Subtle cardinal Monotonically far Chromatic number Prikry-type forcing transformations Rado's conjecture L-space Reduced Power tensor product graph Diamond-sharp Nonspecial tree P-Ideal Dichotomy square specializable Souslin tree Generalized Clubs Subtle tree property Forcing Subadditive diamond star Respecting tree Commutative cancellative semigroups projective Boolean algebra super-Souslin tree Souslin Tree Erdos Cardinal Successor of Singular Cardinal Postprocessing function Almost-disjoint family full tree Cardinal function SNR Distributive tree Whitehead Problem Singular cardinals combinatorics Poset coloring number weak square Martin's Axiom Hindman's Theorem Absoluteness Universal Sequences incompactness nonmeager set Uniformly coherent Filter reflection Weakly compact cardinal Ostaszewski square Uniformly homogeneous higher Baire space weak Kurepa tree stationary reflection Ulam matrix Was Ulam right? Knaster and friends Constructible Universe Hereditarily Lindelöf space Uniformization Rainbow sets Almost countably chromatic Knaster Ascending path regressive Souslin tree Chang's conjecture Small forcing ccc Strong coloring perfectly normal Well-behaved magma Antichain Sigma-Prikry Analytic sets
Tag Archives: Respecting tree
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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Square with built-in diamond-plus
Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in $L$ for every infinite cardinal. As an application, we prove that … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting tree, square, xbox
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Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading
