Archives
Keywords
Singular Density Jonsson cardinal Slim tree Antichain Diamond Singular cardinals combinatorics higher Baire space weak diamond sap Generalized Clubs PFA middle diamond Countryman line Almost-disjoint family Axiom R O-space Reduced Power Closed coloring approachability ideal Prikry-type forcing positive partition relation nonmeager set Dushnik-Miller b-scale Parameterized proxy principle coloring number Ostaszewski square Uniformly coherent Aronszajn tree Large Cardinals super-Souslin tree Absoluteness Fodor-type reflection Hedetniemi's conjecture 54G20 regressive Souslin tree reflection principles Almost countably chromatic Successor of Regular Cardinal indecomposable filter projective Boolean algebra Partition Relations OCA Respecting tree Microscopic Approach Selective Ultrafilter full tree Dowker space Open Access Forcing Hindman's Theorem Prevalent singular cardinals Subnormal ideal Analytic sets AIM forcing L-space xbox Well-behaved magma weak square Subtle cardinal Martin's Axiom Chromatic number stationary hitting Diamond for trees tensor product graph Was Ulam right? P-Ideal Dichotomy Strong coloring Generalized descriptive set theory ccc strongly bounded groups Uniformization Weakly compact cardinal Erdos Cardinal Subadditive Commutative cancellative semigroups Subtle tree property Rainbow sets GMA very good scale diamond star Chang's conjecture free Souslin tree stick Ascent Path Sierpinski's onto mapping principle Constructible Universe HOD incompactness Souslin Tree Singular cofinality weak Kurepa tree Strongly compact cardinal Fat stationary set Iterated forcing Almost Souslin transformations Interval topology on trees Cardinal Invariants Kurepa Hypothesis square principles Fast club Strongly Luzin set Rock n' Roll Small forcing Poset Non-saturation Monotonically far S-Space C-sequence Ascending path Ramsey theory over partitions Intersection model Forcing Axioms Filter reflection free Boolean algebra Amenable C-sequence Nonspecial tree Ulam matrix Cohen real Cardinal function Greatly Mahlo Knaster and friends ZFC construction Forcing with side conditions square Entangled linear order Uniformly homogeneous Sigma-Prikry Club Guessing SNR Erdos-Hajnal graphs Foundations Commutative projection system Distributive tree Sakurai's Bell inequality Whitehead Problem Vanishing levels Successor of Singular Cardinal Reflecting stationary set Universal Sequences Diamond-sharp Precaliber perfectly normal Mandelbrot set polarized partition relation stationary reflection Ineffable cardinal specializable Souslin tree PFA(S)[S] Coherent tree Knaster Partition relations for trees unbounded function club_AD Square-Brackets Partition Relations Postprocessing function Minimal Walks Hereditarily Lindelöf space Lipschitz reduction countably metacompact Luzin set Shelah's Strong Hypothesis Local Club Condensation. Rado's conjecture
Tag Archives: weak square
A remark on Schimmerling’s question
Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading
Weak square and stationary reflection
Joint work with Gunter Fuchs. Abstract. It is well-known that the square principle $\square_\lambda$ entails the existence of a non-reflecting stationary subset of $\lambda^+$, whereas the weak square principle $\square^*_\lambda$ does not. Here we show that if $\mu^{cf(\lambda)}<\lambda$ for all $\mu<\lambda$, … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, stationary reflection, weak square
Leave a comment
The search for diamonds
Abstract: This is a review I wrote for the Bulletin of Symbolic Logic on the following papers: Saharon Shelah, Middle Diamond, Archive for Mathematical Logic, vol. 44 (2005), pp. 527–560. Saharon Shelah, Diamonds, Proceedings of the American Mathematical Society, vol. … Continue reading
Posted in Publications, Reviews, Squares and Diamonds
Tagged Diamond, middle diamond, weak diamond, weak square
1 Comment
A cofinality-preserving small forcing may introduce a special Aronszajn tree
Extended Abstract: Shelah proved that Cohen forcing introduces a Souslin tree; Jensen proved that a c.c.c. forcing may consistently add a Kurepa tree; Todorcevic proved that a Knaster poset may already force the Kurepa hypothesis; Irrgang introduced a c.c.c. notion … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E04, 03E05, 03E35, Aronszajn tree, Small forcing, Successor of Singular Cardinal, weak square
Leave a comment
Young Researchers in Set Theory, March 2011
These are the slides of a talk I gave at the Young Researchers in Set Theory 2011 meeting (Königswinter, 21–25 March 2011). Talk Title: Around Jensen’s square principle Abstract: Jensen‘s square principle for a cardinal $\lambda$ asserts the existence of a particular ladder … Continue reading
