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