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