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