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Analytic sets Generalized Clubs incompactness Almost countably chromatic strongly bounded groups PFA HOD Strong coloring Forcing with side conditions Commutative cancellative semigroups L-space Fast club Souslin Tree nonmeager set Ostaszewski square Countryman line PFA(S)[S] Successor of Regular Cardinal Partition relations for trees Subtle tree property Greatly Mahlo ZFC construction Rock n' Roll Rado's conjecture Partition Relations Fodor-type reflection Erdos Cardinal Weakly compact cardinal Dushnik-Miller Successor of Singular Cardinal Subadditive Closed coloring stick full tree free Boolean algebra Subtle cardinal Antichain O-space projective Boolean algebra countably metacompact stationary hitting free Souslin tree Erdos-Hajnal graphs square Fat stationary set Axiom R Uniformly coherent Luzin set polarized partition relation Constructible Universe Absoluteness Minimal Walks coloring number tensor product graph OCA weak square Generalized descriptive set theory Martin's Axiom Non-saturation Small forcing Large Cardinals square principles Interval topology on trees Open Access weak diamond Coherent tree Club Guessing Hedetniemi's conjecture Shelah's Strong Hypothesis regressive Souslin tree transformations Strongly compact cardinal Whitehead Problem Uniformization Cardinal Invariants indecomposable filter Reflecting stationary set Uniformly homogeneous Postprocessing function Sigma-Prikry reflection principles weak Kurepa tree Dowker space Well-behaved magma C-sequence Knaster and friends Singular Density Singular cardinals combinatorics approachability ideal Cardinal function Cohen real very good scale higher Baire space perfectly normal unbounded function super-Souslin tree Ascent Path Precaliber SNR Ineffable cardinal Sakurai's Bell inequality b-scale Reduced Power GMA AIM forcing Vanishing levels Local Club Condensation. Chang's conjecture Chromatic number Aronszajn tree Lipschitz reduction Hereditarily Lindelöf space Mandelbrot set Monotonically far Selective Ultrafilter xbox Kurepa Hypothesis positive partition relation Rainbow sets Square-Brackets Partition Relations Subnormal ideal Almost Souslin Was Ulam right? Parameterized proxy principle Ramsey theory over partitions Forcing Filter reflection P-Ideal Dichotomy Ulam matrix specializable Souslin tree club_AD Strongly Luzin set Universal Sequences 54G20 Jonsson cardinal Distributive tree middle diamond ccc Almost-disjoint family sap Knaster Ascending path diamond star Sierpinski's onto mapping principle Hindman's Theorem Respecting tree Diamond for trees Amenable C-sequence Commutative projection system Entangled linear order Prevalent singular cardinals Poset Prikry-type forcing S-Space Microscopic Approach Iterated forcing stationary reflection Diamond-sharp Singular cofinality Intersection model Forcing Axioms Slim tree Diamond Foundations Nonspecial tree
Tag Archives: unbounded function
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
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … Continue reading
The 15th International Workshop on Set Theory in Luminy, September 2019
I gave an invited talk at the 15th International Workshop on Set Theory in Luminy in Marseille, September 2019. Talk Title: Chain conditions, unbounded colorings and the C-sequence spectrum. Abstract: The productivity of the $\kappa$-chain condition, where $\kappa$ is a regular, … Continue reading
Posted in Invited Talks
Tagged Closed coloring, Knaster, Precaliber, stationary reflection, unbounded function
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Knaster and friends I: Closed colorings and precalibers
Joint work with Chris Lambie-Hanson. Abstract. The productivity of the $\kappa$-chain condition, where $\kappa$ is a regular, uncountable cardinal, has been the focus of a great deal of set-theoretic research. In the 1970s, consistent examples of $\kappa$-cc posets whose squares … Continue reading
