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