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