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