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