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