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