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