Archives
Keywords
Axiom R club_AD Non-saturation P-Ideal Dichotomy Diamond-sharp Sigma-Prikry Subadditive Cardinal function Poset Ascent Path weak square Shelah's Strong Hypothesis Prevalent singular cardinals Singular cofinality HOD Open Access Diamond Fodor-type reflection Postprocessing function PFA Almost Souslin Knaster and friends Absoluteness Parameterized proxy principle Reflecting stationary set middle diamond Ramsey theory over partitions Martin's Axiom PFA(S)[S] Sierpinski's onto mapping principle Luzin set tensor product graph Cardinal Invariants indecomposable filter Local Club Condensation. Erdos-Hajnal graphs Fast club O-space Fat stationary set weak diamond Dowker space sap unbounded function Lipschitz reduction coloring number Minimal Walks Ulam matrix polarized partition relation 54G20 Hereditarily Lindelöf space Intersection model Selective Ultrafilter Weakly compact cardinal Filter reflection Analytic sets Large Cardinals positive partition relation Greatly Mahlo Whitehead Problem regressive Souslin tree Chromatic number Rock n' Roll Souslin Tree Strongly Luzin set super-Souslin tree full tree stick Singular cardinals combinatorics Respecting tree Was Ulam right? approachability ideal stationary hitting Sakurai's Bell inequality C-sequence Ostaszewski square Slim tree Almost-disjoint family Partition Relations square Vanishing levels GMA strongly bounded groups Countryman line free Souslin tree Dushnik-Miller transformations Reduced Power Cohen real SNR Jonsson cardinal Aronszajn tree Subtle cardinal Subtle tree property specializable Souslin tree Monotonically far b-scale Strongly compact cardinal Closed coloring weak Kurepa tree Successor of Singular Cardinal L-space Uniformly coherent Small forcing Well-behaved magma Commutative cancellative semigroups Foundations Erdos Cardinal Chang's conjecture xbox Amenable C-sequence diamond star Uniformly homogeneous free Boolean algebra countably metacompact Forcing Forcing Axioms Kurepa Hypothesis Strong coloring Uniformization ZFC construction Almost countably chromatic Hedetniemi's conjecture Knaster very good scale square principles AIM forcing reflection principles Interval topology on trees Singular Density Generalized Clubs Square-Brackets Partition Relations Rainbow sets perfectly normal Constructible Universe Coherent tree nonmeager set Universal Sequences Mandelbrot set Rado's conjecture Successor of Regular Cardinal Commutative projection system Diamond for trees Precaliber Hindman's Theorem Forcing with side conditions Generalized descriptive set theory OCA Ascending path stationary reflection Partition relations for trees Entangled linear order Microscopic Approach Club Guessing Nonspecial tree Subnormal ideal Iterated forcing projective Boolean algebra Antichain Distributive tree Ineffable cardinal higher Baire space ccc Prikry-type forcing incompactness S-Space
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
