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Chang's conjecture Luzin set ccc PFA(S)[S] Mandelbrot set Souslin Tree Postprocessing function Greatly Mahlo Square-Brackets Partition Relations Coherent tree weak square Diamond for trees Closed coloring Countryman line Vanishing levels free Boolean algebra coloring number Amenable C-sequence Sakurai's Bell inequality weak Kurepa tree Constructible Universe Ascent Path specializable Souslin tree Prevalent singular cardinals C-sequence Nonspecial tree Absoluteness nonmeager set Analytic sets Successor of Regular Cardinal Sigma-Prikry stick positive partition relation Dowker space Jonsson cardinal Almost Souslin Local Club Condensation. countably metacompact Cardinal function Microscopic Approach middle diamond Singular cardinals combinatorics Subtle tree property Successor of Singular Cardinal Strongly compact cardinal square Minimal Walks Forcing Prikry-type forcing Axiom R diamond star Aronszajn tree stationary reflection Iterated forcing Rado's conjecture Knaster and friends strongly bounded groups Erdos-Hajnal graphs Open Access stationary hitting OCA Selective Ultrafilter Large Cardinals weak diamond regressive Souslin tree Fodor-type reflection Weakly compact cardinal Dushnik-Miller HOD 54G20 polarized partition relation Chromatic number Diamond-sharp indecomposable ultrafilter Commutative cancellative semigroups club_AD free Souslin tree Respecting tree sap Reflecting stationary set Rainbow sets Uniformization Lipschitz reduction Small forcing Non-saturation full tree S-Space Hindman's Theorem Ineffable cardinal Was Ulam right? Distributive tree Intersection model unbounded function xbox Well-behaved magma Antichain AIM forcing Whitehead Problem higher Baire space ZFC construction Sierpinski's onto mapping principle Uniformly coherent Filter reflection tensor product graph P-Ideal Dichotomy Precaliber Forcing Axioms transformations Ostaszewski square GMA Generalized descriptive set theory Generalized Clubs Erdos Cardinal PFA incompactness Knaster Cohen real Strongly Luzin set Reduced Power Partition Relations Uniformly homogeneous Hereditarily Lindelöf space Strong coloring Universal Sequences Singular cofinality Rock n' Roll very good scale approachability ideal Shelah's Strong Hypothesis Club Guessing square principles super-Souslin tree Ulam matrix Slim tree Almost-disjoint family Subtle cardinal Kurepa Hypothesis Diamond SNR Hedetniemi's conjecture b-scale Martin's Axiom Singular Density L-space Subnormal ideal Commutative projection system O-space Cardinal Invariants Ramsey theory over partitions Foundations Poset Parameterized proxy principle Fast club Subadditive Fat stationary set Almost countably chromatic reflection principles projective Boolean algebra
Tag Archives: Uniformization
Generalizations of Martin’s Axiom and the well-met condition
Recall that Martin’s Axiom asserts that for every partial order
The uniformization property for
Given a subset of a regular uncountable cardinal
The uniformization property for
Given a subset of a regular uncountable cardinal
c.c.c. forcing without combinatorics
In this post, we shall discuss a short paper by Alan Mekler from 1984, concerning a non-combinatorial verification of the c.c.c. property for forcing notions. Recall that a notion of forcing
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
On guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading
