Archives
Keywords
Singular Density stationary reflection nonmeager set Almost countably chromatic Singular cardinals combinatorics stick Uniformly homogeneous Interval topology on trees polarized partition relation countably metacompact Knaster Amenable C-sequence Small forcing Intersection model Filter reflection Nonspecial tree O-space specializable Souslin tree Rock n' Roll indecomposable filter Kurepa Hypothesis L-space Poset Mandelbrot set Greatly Mahlo Erdos Cardinal Ulam matrix Partition Relations Diamond for trees free Boolean algebra Prevalent singular cardinals Square-Brackets Partition Relations reflection principles Sierpinski's onto mapping principle SNR club_AD Souslin Tree Fodor-type reflection Chromatic number Monotonically far tensor product graph Whitehead Problem Absoluteness Ostaszewski square Aronszajn tree transformations weak Kurepa tree Cardinal function Almost-disjoint family Diamond Antichain Postprocessing function Erdos-Hajnal graphs Well-behaved magma Martin's Axiom S-Space Forcing with side conditions Shelah's Strong Hypothesis incompactness Commutative projection system Ineffable cardinal Rainbow sets C-sequence Selective Ultrafilter projective Boolean algebra Distributive tree weak square Uniformization approachability ideal Iterated forcing free Souslin tree Generalized descriptive set theory Weakly compact cardinal full tree Successor of Regular Cardinal Foundations Uniformly coherent Lipschitz reduction Cardinal Invariants Microscopic Approach Universal Sequences Open Access Rado's conjecture square principles Generalized Clubs Reduced Power Subtle tree property Analytic sets regressive Souslin tree Sigma-Prikry Strongly compact cardinal Coherent tree 54G20 ZFC construction P-Ideal Dichotomy Precaliber middle diamond Successor of Singular Cardinal b-scale Strong coloring HOD Axiom R Ascent Path Knaster and friends square Subtle cardinal Hindman's Theorem Reflecting stationary set Chang's conjecture Local Club Condensation. Club Guessing Luzin set Cohen real PFA Fat stationary set Countryman line Fast club Subnormal ideal Forcing Axioms Dushnik-Miller Hedetniemi's conjecture coloring number Dowker space ccc stationary hitting Entangled linear order Minimal Walks sap Slim tree Prikry-type forcing super-Souslin tree Forcing GMA Vanishing levels diamond star OCA Subadditive Sakurai's Bell inequality Jonsson cardinal perfectly normal Closed coloring Strongly Luzin set Constructible Universe Hereditarily Lindelöf space AIM forcing strongly bounded groups Was Ulam right? Ramsey theory over partitions weak diamond PFA(S)[S] unbounded function Partition relations for trees Almost Souslin Respecting tree Parameterized proxy principle Non-saturation higher Baire space very good scale xbox Commutative cancellative semigroups Singular cofinality Large Cardinals Diamond-sharp positive partition relation Ascending path
Tag Archives: 06A07
Antichains in partially ordered sets of singular cofinality
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The main result of of this … Continue reading
Posted in Publications, Singular Cardinals Combinatorics
Tagged 03E04, 03E35, 06A07, Antichain, Poset, Singular cofinality
Leave a comment