Archives
Keywords
Uniformization Rock n' Roll Martin's Axiom free Boolean algebra Postprocessing function Commutative projection system Cardinal function C-sequence Cardinal Invariants SNR free Souslin tree Universal Sequences Ostaszewski square transformations Luzin set Sakurai's Bell inequality Jonsson cardinal Erdos-Hajnal graphs stick Successor of Singular Cardinal higher Baire space Diamond-sharp Reflecting stationary set stationary hitting full tree Subtle cardinal polarized partition relation PFA Constructible Universe Selective Ultrafilter Slim tree Sierpinski's onto mapping principle Ascent Path Aronszajn tree Strongly compact cardinal Ulam matrix very good scale L-space Poset GMA tensor product graph Generalized descriptive set theory Antichain Uniformly homogeneous weak diamond Successor of Regular Cardinal nonmeager set Erdos Cardinal Lipschitz reduction indecomposable ultrafilter Hindman's Theorem Dowker space P-Ideal Dichotomy Prikry-type forcing Sigma-Prikry strongly bounded groups Well-behaved magma Foundations Chang's conjecture regressive Souslin tree Commutative cancellative semigroups Weakly compact cardinal positive partition relation Kurepa Hypothesis Souslin Tree incompactness Knaster Square-Brackets Partition Relations Club Guessing ccc Chromatic number b-scale Subadditive Dushnik-Miller Was Ulam right approachability ideal Whitehead Problem O-space square principles specializable Souslin tree reflection principles xbox weak square projective Boolean algebra Respecting tree Fast club Small forcing Distributive tree Precaliber unbounded function stationary reflection Singular cofinality Singular cardinals combinatorics Knaster and friends Open Access Strong coloring Ineffable cardinal Parameterized proxy principle Uniformly coherent HOD Generalized Clubs Rado's conjecture Forcing Axioms super-Souslin tree Absoluteness Almost countably chromatic AIM forcing coloring number 54G20 Analytic sets Local Club Condensation. Partition Relations Shelah's Strong Hypothesis S-Space Non-saturation Fat stationary set Cohen real Subtle tree property Axiom R Hereditarily Lindelöf space club_AD Diamond Filter reflection Large Cardinals Hedetniemi's conjecture Closed coloring square middle diamond Amenable C-sequence Mandelbrot set sap OCA Microscopic Approach ZFC construction diamond star Almost Souslin PFA(S)[S] Reduced Power weak Kurepa tree Prevalent singular cardinals Iterated forcing Nonspecial tree countably metacompact Vanishing levels Intersection model Fodor-type reflection Rainbow sets Countryman line Singular Density Coherent tree Strongly Luzin set Subnormal ideal Minimal Walks Forcing Ramsey theory over partitions Greatly Mahlo Diamond for trees Almost-disjoint family
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 $Vspec(\kappa)$ of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. The latter is an invariant in … Continue reading
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
