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