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Ostaszewski square Forcing with side conditions Entangled linear order Cardinal function ZFC construction Singular cofinality Successor of Singular Cardinal strongly bounded groups Distributive tree Diamond-sharp Square-Brackets Partition Relations Dowker space incompactness super-Souslin tree Rock n' Roll SNR Singular Density tensor product graph Minimal Walks S-Space Poset GMA Greatly Mahlo Chang's conjecture very good scale Commutative cancellative semigroups Hindman's Theorem transformations Reflecting stationary set Interval topology on trees Ascending path Analytic sets countably metacompact Aronszajn tree Constructible Universe full tree Generalized Clubs Subnormal ideal weak square xbox projective Boolean algebra Ulam matrix stationary hitting Knaster and friends specializable Souslin tree Ramsey theory over partitions reflection principles Almost-disjoint family Fast club AIM forcing Erdos Cardinal Antichain Precaliber Generalized descriptive set theory sap Uniformization Absoluteness Mandelbrot set Strong coloring regressive Souslin tree Hedetniemi's conjecture Open Access Forcing Local Club Condensation. Monotonically far Microscopic Approach perfectly normal Dushnik-Miller PFA Diamond HOD Postprocessing function Luzin set Forcing Axioms Club Guessing Iterated forcing Countryman line Universal Sequences Almost Souslin unbounded function 54G20 nonmeager set diamond star square principles Ascent Path ccc OCA Well-behaved magma weak diamond PFA(S)[S] Filter reflection Intersection model Uniformly coherent Large Cardinals Respecting tree Successor of Regular Cardinal Cardinal Invariants L-space polarized partition relation Jonsson cardinal coloring number Amenable C-sequence Erdos-Hajnal graphs Coherent tree Subtle cardinal square Non-saturation Cohen real Commutative projection system Small forcing Nonspecial tree Sakurai's Bell inequality Diamond for trees Whitehead Problem Axiom R Sigma-Prikry Rainbow sets Prikry-type forcing O-space Knaster Shelah's Strong Hypothesis Reduced Power free Souslin tree indecomposable filter Prevalent singular cardinals positive partition relation Lipschitz reduction stick Chromatic number Almost countably chromatic approachability ideal Selective Ultrafilter Sierpinski's onto mapping principle Parameterized proxy principle Strongly Luzin set Subadditive higher Baire space Uniformly homogeneous Rado's conjecture C-sequence Singular cardinals combinatorics weak Kurepa tree Ineffable cardinal Hereditarily Lindelöf space stationary reflection Fodor-type reflection Subtle tree property Slim tree Closed coloring Weakly compact cardinal P-Ideal Dichotomy middle diamond club_AD Partition relations for trees Kurepa Hypothesis b-scale Was Ulam right? Souslin Tree Foundations free Boolean algebra Martin's Axiom Strongly compact cardinal Vanishing levels Partition Relations Fat stationary set
Tag Archives: Singular cofinality
Logic in Hungary, August 2005
These are the slides of a contributed talk given at the Logic in Hungary 2005 meeting (Budapest, 5–11 August 2005). Talk Title: On the consistency strength of the Milner-Sauer Conjecture Abstract: In their paper from 1981, after learning about Pouzet‘s theorem that any … Continue reading
Posted in Contributed Talks
Tagged Antichain, Shelah's Strong Hypothesis, Singular cofinality
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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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