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