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