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Parameterized proxy principle Rado's conjecture Chromatic number Forcing Axioms S-Space SNR xbox Square-Brackets Partition Relations polarized partition relation Absoluteness Dushnik-Miller Chang's conjecture middle diamond Minimal Walks countably metacompact Ineffable cardinal b-scale Hereditarily Lindelöf space square Non-saturation Hedetniemi's conjecture Fast club sap Ascent Path Rainbow sets regressive Souslin tree Well-behaved magma Generalized Clubs Microscopic Approach Aronszajn tree Jonsson cardinal Cardinal function diamond star Greatly Mahlo Almost Souslin Diamond-sharp Singular cardinals combinatorics Universal Sequences Singular cofinality weak diamond Subnormal ideal Kurepa Hypothesis Prikry-type forcing Lipschitz reduction PFA(S)[S] L-space Local Club Condensation. HOD PFA Successor of Singular Cardinal Almost countably chromatic OCA AIM forcing Almost-disjoint family free Boolean algebra reflection principles Successor of Regular Cardinal Rock n' Roll full tree transformations Coherent tree Knaster Strongly Luzin set Strong coloring Luzin set 54G20 Ostaszewski square Selective Ultrafilter Uniformly homogeneous free Souslin tree Martin's Axiom Axiom R Commutative cancellative semigroups Uniformly coherent C-sequence Forcing Iterated forcing Vanishing levels Souslin Tree unbounded function Distributive tree nonmeager set super-Souslin tree Dowker space Erdos-Hajnal graphs Large Cardinals Mandelbrot set Subtle tree property Slim tree Postprocessing function positive partition relation Generalized descriptive set theory Reflecting stationary set projective Boolean algebra Amenable C-sequence P-Ideal Dichotomy weak square tensor product graph Club Guessing Ulam matrix Ramsey theory over partitions Singular Density Filter reflection O-space Uniformization higher Baire space Sierpinski's onto mapping principle ZFC construction Reduced Power Fat stationary set Cardinal Invariants incompactness Whitehead Problem coloring number approachability ideal Knaster and friends indecomposable ultrafilter Poset Was Ulam right Sigma-Prikry GMA very good scale Sakurai's Bell inequality Partition Relations ccc Subtle cardinal specializable Souslin tree Constructible Universe Cohen real Open Access Diamond for trees Hindman's Theorem Analytic sets Subadditive Erdos Cardinal Diamond Shelah's Strong Hypothesis Foundations Small forcing strongly bounded groups Nonspecial tree stick Closed coloring Antichain stationary hitting Prevalent singular cardinals Fodor-type reflection Weakly compact cardinal Precaliber club_AD square principles stationary reflection
Tag Archives: Uniformization
Generalizations of Martin’s Axiom and the well-met condition
Recall that Martin’s Axiom asserts that for every partial order $\mathbb P$ satisfying c.c.c., and for any family $\mathcal D$ of $<2^{\aleph_0}$ many dense subsets of $\mathbb P$, there exists a directed subset $G$ of $\mathbb P$ such that $G\cap … Continue reading
The uniformization property for $\aleph_2$
Given a subset of a regular uncountable cardinal $S\subseteq\kappa$, $UP_S$ (read: “the uniformization property holds for $S$”) asserts that for every sequence $\overrightarrow f=\langle f_\alpha\mid \alpha\in S\rangle$ satisfying for all $\alpha\in S$: $f_\alpha$ is a 2-valued function; $\text{dom}(f_\alpha)$ is a … Continue reading
The uniformization property for $\aleph_2$
Given a subset of a regular uncountable cardinal $S\subseteq\kappa$, $UP_S$ (read: “the uniformization property holds for $S$”) asserts that for every sequence $\overrightarrow f=\langle f_\alpha\mid \alpha\in S\rangle$ satisfying for all $\alpha\in S$: $f_\alpha$ is a 2-valued function; $\text{dom}(f_\alpha)$ is a … Continue reading
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 $\mathbb P$ is said to satisfy the c.c.c. iff … 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
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