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