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