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