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