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