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