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