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Erdos Cardinal reflection principles Reduced Power Non-saturation S-Space very good scale Analytic sets Coherent tree PFA(S)[S] diamond star Commutative projection system Prikry-type forcing Sakurai's Bell inequality Large Cardinals Closed coloring Subtle tree property specializable Souslin tree Strongly compact cardinal countably metacompact b-scale square principles OCA Whitehead Problem Cohen real Weakly compact cardinal Ostaszewski square Poset Generalized Clubs Lipschitz reduction Successor of Regular Cardinal ccc Foundations Postprocessing function Ascent Path approachability ideal Well-behaved magma regressive Souslin tree 54G20 Fat stationary set HOD Was Ulam right? Rainbow sets weak square Singular cardinals combinatorics stationary hitting stick Hindman's Theorem Commutative cancellative semigroups O-space polarized partition relation super-Souslin tree unbounded function Cardinal function ZFC construction Sigma-Prikry Intersection model Reflecting stationary set Chang's conjecture Subnormal ideal Slim tree Minimal Walks PFA L-space Vanishing levels transformations higher Baire space Souslin Tree square Uniformization SNR Fast club Square-Brackets Partition Relations Sierpinski's onto mapping principle Precaliber incompactness club_AD Local Club Condensation. Iterated forcing full tree Distributive tree Microscopic Approach projective Boolean algebra Uniformly coherent Shelah's Strong Hypothesis Successor of Singular Cardinal nonmeager set Kurepa Hypothesis GMA Hedetniemi's conjecture middle diamond Prevalent singular cardinals weak Kurepa tree Erdos-Hajnal graphs Absoluteness xbox Chromatic number Rock n' Roll Aronszajn tree Martin's Axiom Ineffable cardinal Small forcing Singular cofinality sap positive partition relation Countryman line Fodor-type reflection stationary reflection weak diamond Forcing Axioms Generalized descriptive set theory Respecting tree indecomposable ultrafilter Strong coloring Dowker space Mandelbrot set Almost-disjoint family Greatly Mahlo Forcing Knaster and friends coloring number Jonsson cardinal Strongly Luzin set Knaster Selective Ultrafilter Uniformly homogeneous Open Access AIM forcing Rado's conjecture Ulam matrix Ramsey theory over partitions Subadditive Almost countably chromatic Diamond-sharp Hereditarily Lindelöf space Axiom R free Boolean algebra Nonspecial tree Diamond for trees Dushnik-Miller Antichain tensor product graph Subtle cardinal Almost Souslin Universal Sequences C-sequence Filter reflection Club Guessing P-Ideal Dichotomy Singular Density Amenable C-sequence Constructible Universe Luzin set strongly bounded groups Parameterized proxy principle free Souslin tree Diamond Cardinal Invariants Partition Relations
Blog Archives
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
A club guessing toolbox I
Joint work with Tanmay Inamdar. Abstract. Club guessing principles were introduced by Shelah as a weakening of Jensen’s diamond. Most spectacularly, they were used to prove Shelah’s ZFC bound on the power of the first singular cardinal. These principles have … Continue reading
Was Ulam right? II: Small width and general ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Sierpinski-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular, improving upon Ulam’s theorem and its extension … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E35, 03E55, C-sequence, Open Access, Subnormal ideal, Ulam matrix, Was Ulam right?
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Was Ulam right? I: Basic theory and subnormal ideals
Joint work with Tanmay Inamdar. Abstract. We introduce various coloring principles which generalize the so-called onto mapping principle of Sierpinski to larger cardinals and general ideals. We prove that these principles capture the notion of an Ulam matrix and allow … Continue reading
