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