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polarized partition relation free Boolean algebra Club Guessing Large Cardinals Singular cofinality Vanishing levels Diamond Coherent tree Chang's conjecture Dushnik-Miller strongly bounded groups Dowker space Commutative projection system Ostaszewski square Subadditive Ascent Path Small forcing free Souslin tree ccc Singular Density Rado's conjecture Universal Sequences regressive Souslin tree Weakly compact cardinal Forcing Sierpinski's onto mapping principle Uniformization Parameterized proxy principle weak Kurepa tree nonmeager set square indecomposable ultrafilter higher Baire space approachability ideal Chromatic number Rainbow sets Cohen real Subtle cardinal Local Club Condensation. Square-Brackets Partition Relations weak square Distributive tree Reduced Power incompactness countably metacompact Aronszajn tree stationary reflection Subtle tree property Reflecting stationary set Hedetniemi's conjecture P-Ideal Dichotomy Respecting tree Almost Souslin Postprocessing function Generalized Clubs Amenable C-sequence Iterated forcing Prevalent singular cardinals 54G20 Ulam matrix Commutative cancellative semigroups Was Ulam right Closed coloring stationary hitting Hindman's Theorem L-space Almost-disjoint family transformations PFA(S)[S] Fat stationary set Singular cardinals combinatorics O-space Mandelbrot set coloring number xbox Absoluteness Luzin set Ramsey theory over partitions ZFC construction Well-behaved magma Poset weak diamond positive partition relation tensor product graph sap Kurepa Hypothesis Open Access Rock n' Roll Cardinal function Generalized descriptive set theory specializable Souslin tree full tree OCA Almost countably chromatic Hereditarily Lindelöf space middle diamond Cardinal Invariants Countryman line Minimal Walks Erdos Cardinal Precaliber Greatly Mahlo Subnormal ideal Nonspecial tree Jonsson cardinal Microscopic Approach Successor of Regular Cardinal Foundations Filter reflection very good scale Partition Relations club_AD super-Souslin tree S-Space Ineffable cardinal C-sequence Intersection model diamond star Knaster reflection principles Lipschitz reduction projective Boolean algebra Shelah's Strong Hypothesis Diamond-sharp unbounded function Prikry-type forcing Diamond for trees Sakurai's Bell inequality GMA Successor of Singular Cardinal Souslin Tree SNR Axiom R Constructible Universe Uniformly coherent PFA HOD Fodor-type reflection Knaster and friends square principles Forcing Axioms Selective Ultrafilter Strong coloring Antichain Martin's Axiom Slim tree Strongly compact cardinal Non-saturation Sigma-Prikry Whitehead Problem AIM forcing Erdos-Hajnal graphs Strongly Luzin set Analytic sets Fast club Uniformly homogeneous b-scale stick
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
Posted in Compactness, Preprints
Tagged Forcing Axioms, indecomposable ultrafilter, Subadditive, unbounded function
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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, Preprints
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, 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
