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