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Strongly Luzin set Successor of Singular Cardinal Generalized Clubs Microscopic Approach Selective Ultrafilter Subnormal ideal Was Ulam right? Chang's conjecture P-Ideal Dichotomy Axiom R Well-behaved magma Fat stationary set Countryman line Rock n' Roll Subtle cardinal Parameterized proxy principle Subadditive unbounded function GMA Partition Relations Universal Sequences Vanishing levels Poset Diamond for trees Subtle tree property Absoluteness full tree super-Souslin tree L-space Dowker space Knaster Almost-disjoint family b-scale Chromatic number Respecting tree indecomposable ultrafilter Ramsey theory over partitions Generalized descriptive set theory incompactness PFA Singular cardinals combinatorics Fast club Closed coloring Prikry-type forcing Ascent Path stick Mandelbrot set club_AD Diamond Diamond-sharp strongly bounded groups Cohen real weak diamond Commutative cancellative semigroups Minimal Walks Hindman's Theorem Sierpinski's onto mapping principle Weakly compact cardinal Jonsson cardinal Kurepa Hypothesis HOD higher Baire space Slim tree Erdos Cardinal Strongly compact cardinal Hereditarily Lindelöf space reflection principles Dushnik-Miller Analytic sets Fodor-type reflection square Hedetniemi's conjecture tensor product graph Precaliber Filter reflection Small forcing Uniformly homogeneous Luzin set Constructible Universe projective Boolean algebra Sigma-Prikry Cardinal Invariants Ostaszewski square square principles Rado's conjecture Singular cofinality Large Cardinals Nonspecial tree Sakurai's Bell inequality Commutative projection system Postprocessing function stationary reflection positive partition relation Forcing PFA(S)[S] regressive Souslin tree very good scale OCA weak Kurepa tree Singular Density Greatly Mahlo Erdos-Hajnal graphs specializable Souslin tree ccc Successor of Regular Cardinal Local Club Condensation. Almost countably chromatic Club Guessing Open Access Shelah's Strong Hypothesis S-Space AIM forcing polarized partition relation Non-saturation countably metacompact C-sequence 54G20 Ineffable cardinal free Souslin tree Foundations sap Antichain Martin's Axiom Whitehead Problem Souslin Tree diamond star Square-Brackets Partition Relations Reflecting stationary set Knaster and friends Reduced Power Rainbow sets Prevalent singular cardinals Strong coloring Amenable C-sequence Uniformly coherent Forcing Axioms Ulam matrix middle diamond Lipschitz reduction xbox Intersection model approachability ideal Iterated forcing Cardinal function Aronszajn tree Uniformization O-space SNR stationary hitting nonmeager set coloring number Coherent tree transformations Distributive tree ZFC construction Almost Souslin free Boolean algebra weak square
Category Archives: Open Problems
Dushnik-Miller for regular cardinals (part 1)
This is the first out of a series of posts on the following theorem. Theorem (Erdos-Dushnik-Miller, 1941). For every infinite cardinal
The order-type of clubs in a square sequence
Recall Jensen’s notion of square: Definition (Jensen): For an infinite cardinal
Jensen’s diamond principle and its relatives
This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading
