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