Archives
Keywords
Reduced Power Prevalent singular cardinals Knaster middle diamond Axiom R PFA PFA(S)[S] Subtle cardinal GMA countably metacompact transformations weak diamond Fodor-type reflection Postprocessing function ccc free Boolean algebra 54G20 free Souslin tree Fast club S-Space Strong coloring Parameterized proxy principle Subnormal ideal Ulam matrix Diamond for trees regressive Souslin tree Partition Relations Reflecting stationary set Souslin Tree Distributive tree Forcing square Cardinal Invariants Forcing Axioms Successor of Singular Cardinal Dushnik-Miller Large Cardinals Monotonically far tensor product graph strongly bounded groups sap incompactness P-Ideal Dichotomy AIM forcing Mandelbrot set Filter reflection Sierpinski's onto mapping principle SNR reflection principles L-space Cardinal function Singular cofinality stick Hedetniemi's conjecture coloring number square principles Slim tree Entangled linear order Poset Partition relations for trees Ineffable cardinal Commutative cancellative semigroups Jonsson cardinal Absoluteness Sigma-Prikry very good scale Ascent Path O-space Erdos-Hajnal graphs Vanishing levels Generalized descriptive set theory perfectly normal Uniformly homogeneous Rainbow sets positive partition relation weak square Strongly Luzin set Diamond Singular Density Chromatic number Erdos Cardinal Chang's conjecture Singular cardinals combinatorics Almost countably chromatic Cohen real Subadditive weak Kurepa tree stationary hitting higher Baire space Prikry-type forcing Strongly compact cardinal Uniformly coherent Diamond-sharp projective Boolean algebra Aronszajn tree Sakurai's Bell inequality Dowker space super-Souslin tree ZFC construction approachability ideal Intersection model indecomposable filter Knaster and friends Amenable C-sequence Iterated forcing Hindman's Theorem Selective Ultrafilter Minimal Walks Constructible Universe polarized partition relation specializable Souslin tree Generalized Clubs Coherent tree Countryman line Well-behaved magma club_AD Fat stationary set Subtle tree property Luzin set Successor of Regular Cardinal OCA Greatly Mahlo nonmeager set Ascending path Square-Brackets Partition Relations Martin's Axiom Ramsey theory over partitions Rock n' Roll Universal Sequences Rado's conjecture Almost Souslin Club Guessing Commutative projection system Local Club Condensation. xbox Lipschitz reduction Respecting tree Precaliber Shelah's Strong Hypothesis Analytic sets Weakly compact cardinal Ostaszewski square Closed coloring diamond star Hereditarily Lindelöf space stationary reflection Forcing with side conditions HOD Nonspecial tree Small forcing Foundations Kurepa Hypothesis Microscopic Approach Uniformization Non-saturation Was Ulam right? full tree Open Access Almost-disjoint family Antichain Whitehead Problem Interval topology on trees unbounded function C-sequence b-scale
Tag Archives: Strong coloring
Conference in honor of Saharon Shelah’s 80th birthday
I gave an invited talk at the conference in honor of Shelah’s 80th birthday, July 2025. Talk Title: Marginalia to [Sh:365] Abstract: Solovay famously proved that every stationary subset of a regular uncountable cardinal kappa may be decomposed into kappa … Continue reading
Posted in Invited Talks
Tagged Greatly Mahlo, Strong coloring, Was Ulam right?
Comments Off on Conference in honor of Saharon Shelah’s 80th birthday
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
Posted in Basis problems, Partition Relations, Preprints
Tagged Aronszajn tree, Ascending path, Club Guessing, Countryman line, Entangled linear order, Minimal Walks, Monotonically far, Partition relations for trees, Strong coloring, Subtle tree property, Vanishing levels, ZFC construction
2 Comments
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, Publications
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Open Access, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
3 Comments
Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems
Joint work with Menachem Kojman and Juris Steprāns. Abstract. In this series of papers, we advance Ramsey theory of colorings over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong colorings, and in … Continue reading
Ramsey theory over partitions III: Strongly Luzin sets and partition relations
Joint work with Menachem Kojman and Juris Steprāns. Abstract. The strongest type of coloring of pairs of countable ordinals, gotten by Todorcevic from a strongly Luzin set, is shown to be equivalent to the existence of a nonmeager set of … Continue reading
Transformations of the transfinite plane
Joint work with Jing Zhang. Abstract. We study the existence of transformations of the transfinite plane that allow one to reduce Ramsey-theoretic statements concerning uncountable Abelian groups into classical partition relations for uncountable cardinals. To exemplify: we prove that for every … Continue reading
