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xbox full tree Martin's Axiom Countryman line Diamond Generalized Clubs Weakly compact cardinal Generalized descriptive set theory P-Ideal Dichotomy Amenable C-sequence GMA Chang's conjecture Diamond-sharp transformations square principles approachability ideal Forcing with side conditions polarized partition relation specializable Souslin tree sap Sigma-Prikry Whitehead Problem Minimal Walks Cardinal function Chromatic number Diamond for trees middle diamond Slim tree HOD Strongly Luzin set Ramsey theory over partitions C-sequence Reflecting stationary set Monotonically far stationary hitting Ineffable cardinal Foundations Ascending path Greatly Mahlo incompactness Prikry-type forcing OCA Poset Parameterized proxy principle Distributive tree Large Cardinals Prevalent singular cardinals very good scale free Souslin tree Knaster and friends Strong coloring Rainbow sets Successor of Regular Cardinal countably metacompact b-scale Shelah's Strong Hypothesis Subtle tree property Intersection model Iterated forcing Universal Sequences Knaster Singular Density Nonspecial tree Local Club Condensation. ccc square Club Guessing Hedetniemi's conjecture strongly bounded groups Aronszajn tree Ostaszewski square Almost Souslin weak diamond club_AD Jonsson cardinal weak square Successor of Singular Cardinal Mandelbrot set Forcing nonmeager set Precaliber higher Baire space Luzin set diamond star super-Souslin tree Singular cofinality regressive Souslin tree Almost countably chromatic PFA(S)[S] Antichain Absoluteness Hereditarily Lindelöf space Sierpinski's onto mapping principle Entangled linear order Uniformization Open Access Lipschitz reduction stationary reflection projective Boolean algebra AIM forcing Forcing Axioms Constructible Universe Was Ulam right? Reduced Power Cardinal Invariants Square-Brackets Partition Relations Analytic sets Souslin Tree perfectly normal Singular cardinals combinatorics tensor product graph S-Space Dowker space Subtle cardinal unbounded function L-space SNR Well-behaved magma Cohen real ZFC construction Uniformly coherent Non-saturation Closed coloring Fodor-type reflection Uniformly homogeneous Fast club Small forcing Strongly compact cardinal Selective Ultrafilter Interval topology on trees reflection principles Partition relations for trees PFA Subnormal ideal Postprocessing function Sakurai's Bell inequality coloring number Fat stationary set Respecting tree positive partition relation Axiom R Filter reflection weak Kurepa tree Ascent Path Coherent tree Almost-disjoint family Kurepa Hypothesis free Boolean algebra Microscopic Approach 54G20 Rado's conjecture Dushnik-Miller indecomposable filter Erdos-Hajnal graphs Subadditive Partition Relations Rock n' Roll stick Erdos Cardinal Commutative projection system Vanishing levels Hindman's Theorem Commutative cancellative semigroups O-space Ulam matrix
Tag Archives: Subadditive
Squares, ultrafilters and forcing axioms
Joint work with Chris Lambie-Hanson and Jing Zhang. Abstract. We study the interplay of the three families of combinatorial objects or principles. Specifically, we show the following. Strong forcing axioms, in general incompatible with the existence of indexed squares, can … Continue reading
A Shelah group in ZFC
Joint work with Márk Poór. Abstract. In a paper from 1980, Shelah constructed an uncountable group all of whose proper subgroups are countable. Assuming the continuum hypothesis, he constructed an uncountable group $G$ that moreover admits an integer $n$ satisfying … Continue reading
Posted in Groups, Publications
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Open Access, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
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Knaster and friends III: Subadditive colorings
Joint work with Chris Lambie-Hanson. Abstract. We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals $\theta < \kappa$, the existence … Continue reading
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading
