Archives
Keywords
Club Guessing strongly bounded groups Souslin Tree PFA Parameterized proxy principle Postprocessing function Erdos-Hajnal graphs Strong coloring Whitehead Problem Well-behaved magma Chromatic number O-space GMA perfectly normal Reflecting stationary set Axiom R Strongly Luzin set projective Boolean algebra club_AD Almost countably chromatic Weakly compact cardinal Cardinal function Dowker space Commutative cancellative semigroups C-sequence L-space Foundations weak square Open Access Kurepa Hypothesis Cardinal Invariants Subnormal ideal Hereditarily Lindelöf space Uniformly homogeneous Ascending path weak Kurepa tree Fat stationary set incompactness Almost Souslin Amenable C-sequence Singular cofinality higher Baire space Local Club Condensation. Forcing Forcing Axioms Singular cardinals combinatorics Distributive tree regressive Souslin tree unbounded function stick Small forcing Rainbow sets Square-Brackets Partition Relations xbox square principles diamond star Chang's conjecture Ineffable cardinal positive partition relation SNR Monotonically far Diamond-sharp Fast club full tree ccc Hedetniemi's conjecture Lipschitz reduction middle diamond Greatly Mahlo free Boolean algebra Ostaszewski square Uniformization HOD tensor product graph Closed coloring PFA(S)[S] Partition Relations Aronszajn tree stationary reflection Knaster Successor of Singular Cardinal 54G20 Subadditive Coherent tree Minimal Walks Diamond Cohen real Commutative projection system Mandelbrot set stationary hitting countably metacompact weak diamond Absoluteness Shelah's Strong Hypothesis Filter reflection Subtle tree property Martin's Axiom free Souslin tree Ascent Path Respecting tree Diamond for trees Interval topology on trees Selective Ultrafilter Iterated forcing b-scale square Strongly compact cardinal Generalized Clubs Dushnik-Miller Vanishing levels Sakurai's Bell inequality specializable Souslin tree Microscopic Approach Countryman line Was Ulam right? Rado's conjecture polarized partition relation Slim tree indecomposable filter ZFC construction Analytic sets Ulam matrix transformations super-Souslin tree reflection principles very good scale Reduced Power Precaliber Sigma-Prikry coloring number Ramsey theory over partitions Prikry-type forcing Jonsson cardinal Constructible Universe Knaster and friends Prevalent singular cardinals Subtle cardinal Universal Sequences Generalized descriptive set theory sap Forcing with side conditions Sierpinski's onto mapping principle Luzin set Successor of Regular Cardinal nonmeager set Fodor-type reflection Nonspecial tree Erdos Cardinal Uniformly coherent Intersection model Singular Density AIM forcing P-Ideal Dichotomy Large Cardinals Non-saturation approachability ideal S-Space Antichain Almost-disjoint family Poset Rock n' Roll OCA Hindman's Theorem Entangled linear order
Blog Archives
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 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
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
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
A forcing axiom deciding the generalized Souslin Hypothesis
Joint work with Chris Lambie-Hanson. Abstract. We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal $\lambda$, … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, Souslin Tree, square, super-Souslin tree
1 Comment
Reflection on the coloring and chromatic numbers
Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Chang's conjecture, Chromatic number, coloring number, Fodor-type reflection, incompactness, Iterated forcing, Parameterized proxy principle, Postprocessing function, Rado's conjecture, square, stationary reflection
2 Comments
