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