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