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