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