Archives
Keywords
Intersection model Luzin set Was Ulam right Strongly Luzin set AIM forcing Poset stick Closed coloring Microscopic Approach L-space b-scale Open Access ZFC construction Almost Souslin Rainbow sets Weakly compact cardinal Sakurai's Bell inequality unbounded function Subnormal ideal GMA Generalized Clubs Kurepa Hypothesis Selective Ultrafilter coloring number Iterated forcing Knaster and friends middle diamond Reflecting stationary set Uniformly homogeneous Singular Density strongly bounded groups Chromatic number Hindman's Theorem 54G20 Souslin Tree Antichain Small forcing Cohen real Martin's Axiom Reduced Power Hereditarily Lindelöf space Successor of Regular Cardinal Local Club Condensation. Slim tree Constructible Universe Universal Sequences Subadditive polarized partition relation Commutative cancellative semigroups Hedetniemi's conjecture Vanishing levels O-space Ramsey theory over partitions super-Souslin tree Singular cofinality Non-saturation free Boolean algebra specializable Souslin tree tensor product graph reflection principles Amenable C-sequence stationary reflection Successor of Singular Cardinal square principles Square-Brackets Partition Relations Jonsson cardinal Commutative projection system OCA Large Cardinals Whitehead Problem Strong coloring Respecting tree Aronszajn tree Lipschitz reduction Well-behaved magma weak square P-Ideal Dichotomy C-sequence Almost countably chromatic Coherent tree Ineffable cardinal weak Kurepa tree countably metacompact stationary hitting SNR Erdos-Hajnal graphs positive partition relation Almost-disjoint family higher Baire space Diamond-sharp Distributive tree square approachability ideal Generalized descriptive set theory Chang's conjecture PFA(S)[S] Fast club Uniformization weak diamond S-Space Dushnik-Miller xbox Cardinal Invariants Prevalent singular cardinals Forcing Axioms PFA Subtle cardinal indecomposable ultrafilter Cardinal function HOD Rado's conjecture Partition Relations Uniformly coherent Parameterized proxy principle Ostaszewski square Strongly compact cardinal sap Axiom R Analytic sets Fodor-type reflection Mandelbrot set Greatly Mahlo Forcing transformations Knaster Fat stationary set Diamond for trees Club Guessing Singular cardinals combinatorics Postprocessing function nonmeager set ccc Dowker space full tree Prikry-type forcing diamond star Diamond Ascent Path regressive Souslin tree Minimal Walks Erdos Cardinal Nonspecial tree Countryman line Sierpinski's onto mapping principle Precaliber very good scale Shelah's Strong Hypothesis free Souslin tree incompactness Sigma-Prikry Filter reflection club_AD projective Boolean algebra Subtle tree property Foundations Absoluteness Rock n' Roll Ulam matrix
Tag Archives: PFA
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
PFA and the tree property at $\aleph_2$
Recall that a poset $\langle T,\le\rangle$ is said to be a $\lambda^+$-Aronszajn tree, if it isomorphic to a poset $(\mathcal T,\subseteq)$ of the form: $\emptyset\in \mathcal T\subseteq{}^{<\lambda^+}\lambda$; Write $\mathcal T_\alpha:=\{\sigma\in\mathcal T\mid \text{dom}(\sigma)=\alpha\}$; for all $\alpha<\lambda^+$, $\mathcal T_\alpha$ has size $\le\lambda$, … Continue reading
