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