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