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