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Hedetniemi's conjecture Fast club Knaster and friends C-sequence unbounded function Singular cardinals combinatorics weak square Iterated forcing Non-saturation HOD stick Chromatic number Postprocessing function Weakly compact cardinal tensor product graph Aronszajn tree free Boolean algebra Diamond-sharp Partition Relations Chang's conjecture ccc b-scale Sierpinski's onto mapping principle Luzin set Universal Sequences Ulam matrix Antichain higher Baire space Kurepa Hypothesis diamond star Singular cofinality GMA indecomposable ultrafilter Martin's Axiom projective Boolean algebra Subtle tree property Almost Souslin countably metacompact ZFC construction Square-Brackets Partition Relations Filter reflection Strong coloring Knaster strongly bounded groups specializable Souslin tree Commutative cancellative semigroups Slim tree Nonspecial tree weak diamond Minimal Walks approachability ideal Reduced Power Successor of Regular Cardinal Rainbow sets Absoluteness Strongly compact cardinal O-space Parameterized proxy principle Open Access L-space square Erdos Cardinal Successor of Singular Cardinal Amenable C-sequence OCA Mandelbrot set nonmeager set Coherent tree Ramsey theory over partitions Generalized descriptive set theory Singular Density Analytic sets free Souslin tree Forcing Strongly Luzin set Fodor-type reflection Cardinal function Hereditarily Lindelöf space Vanishing levels Ascent Path transformations full tree Rado's conjecture Distributive tree regressive Souslin tree middle diamond polarized partition relation Souslin Tree Cohen real S-Space Intersection model xbox Generalized Clubs Subadditive Sigma-Prikry Almost-disjoint family AIM forcing stationary hitting Club Guessing weak Kurepa tree Dushnik-Miller Erdos-Hajnal graphs Was Ulam right Diamond for trees positive partition relation Large Cardinals Almost countably chromatic Constructible Universe sap Respecting tree Local Club Condensation. Small forcing Shelah's Strong Hypothesis Axiom R Cardinal Invariants square principles PFA(S)[S] Prikry-type forcing Ineffable cardinal Sakurai's Bell inequality PFA Diamond super-Souslin tree Lipschitz reduction Uniformly coherent Selective Ultrafilter Forcing Axioms Well-behaved magma Prevalent singular cardinals Dowker space Subnormal ideal Foundations Precaliber very good scale P-Ideal Dichotomy Uniformly homogeneous Poset stationary reflection Rock n' Roll Greatly Mahlo Countryman line Hindman's Theorem Uniformization Fat stationary set Microscopic Approach Jonsson cardinal incompactness Subtle cardinal reflection principles Reflecting stationary set Closed coloring Commutative projection system 54G20 coloring number Whitehead Problem club_AD SNR Ostaszewski square
Tag Archives: 03E45
Square with built-in diamond-plus
Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in $L$ for every infinite cardinal. As an application, we prove that … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting tree, square, xbox
1 Comment
Putting a diamond inside the square
Abstract. By a 35-year-old theorem of Shelah, $\square_\lambda+\diamondsuit(\lambda^+)$ does not imply square-with-built-in-diamond_lambda for regular uncountable cardinals $\lambda$. Here, it is proved that $\square_\lambda+\diamondsuit(\lambda^+)$ is equivalent to square-with-built-in-diamond_lambda for every singular cardinal $\lambda$. Downloads: Citation information: A. Rinot, Putting a diamond inside … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Diamond, square, Successor of Singular Cardinal
1 Comment
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
