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Cohen real Slim tree P-Ideal Dichotomy Club Guessing Rado's conjecture Commutative cancellative semigroups Singular cofinality Hedetniemi's conjecture PFA(S)[S] nonmeager set Diamond-sharp Reflecting stationary set stick strongly bounded groups higher Baire space 54G20 Foundations Souslin Tree Erdos Cardinal Partition Relations approachability ideal Fast club weak diamond Universal Sequences Shelah's Strong Hypothesis Generalized descriptive set theory Cardinal Invariants Subadditive Fodor-type reflection Uniformization Forcing Non-saturation Closed coloring Lipschitz reduction Strong coloring Generalized Clubs Uniformly coherent Subnormal ideal weak square Square-Brackets Partition Relations Successor of Singular Cardinal Was Ulam right Almost Souslin Postprocessing function Nonspecial tree unbounded function tensor product graph coloring number Poset Coherent tree Open Access diamond star Rainbow sets regressive Souslin tree Fat stationary set Subtle tree property Mandelbrot set Prevalent singular cardinals weak Kurepa tree Amenable C-sequence Microscopic Approach Cardinal function Prikry-type forcing Absoluteness countably metacompact PFA Well-behaved magma stationary reflection Distributive tree Ulam matrix Local Club Condensation. Knaster and friends Axiom R full tree Erdos-Hajnal graphs Jonsson cardinal Ascent Path Small forcing AIM forcing Sigma-Prikry incompactness Diamond for trees Minimal Walks Dowker space transformations Sakurai's Bell inequality OCA projective Boolean algebra free Boolean algebra Luzin set O-space Ramsey theory over partitions polarized partition relation Aronszajn tree Ineffable cardinal Dushnik-Miller free Souslin tree Filter reflection Chang's conjecture very good scale indecomposable ultrafilter Antichain Rock n' Roll square principles super-Souslin tree Analytic sets Sierpinski's onto mapping principle C-sequence Precaliber Chromatic number L-space Almost-disjoint family Constructible Universe b-scale ccc Large Cardinals Parameterized proxy principle middle diamond specializable Souslin tree Successor of Regular Cardinal Vanishing levels SNR Forcing Axioms Knaster Kurepa Hypothesis Ostaszewski square GMA Reduced Power stationary hitting Singular Density Greatly Mahlo Selective Ultrafilter xbox positive partition relation Hereditarily Lindelöf space Almost countably chromatic Diamond ZFC construction Singular cardinals combinatorics Strongly Luzin set square Iterated forcing Subtle cardinal Whitehead Problem sap Hindman's Theorem S-Space Uniformly homogeneous club_AD Weakly compact cardinal reflection principles Martin's Axiom HOD
Blog Archives
Square principles
Since the birth of Jensen’s original Square principle, many variations of the principle were introduced and intensively studied. Asaf Karagila suggested me today to put some order into all of these principles. Here is a trial. Definition. A square principle … Continue reading
A Kurepa tree from diamond-plus
Recall that $T$ is said to be a $\kappa$-Kurepa tree if $T$ is a tree of height $\kappa$, whose levels $T_\alpha$ has size $\le|\alpha|$ for co-boundedly many $\alpha<\kappa$, and such that the set of branches of $T$ has size $>\kappa$. … Continue reading
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
