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Fodor-type reflection Precaliber Ostaszewski square Non-saturation Chang's conjecture Forcing Absoluteness O-space Uniformization Weakly compact cardinal incompactness indecomposable ultrafilter Hereditarily Lindelöf space stationary reflection full tree nonmeager set Almost-disjoint family Club Guessing Filter reflection Souslin Tree SNR positive partition relation OCA Square-Brackets Partition Relations Mandelbrot set Was Ulam right Sierpinski's onto mapping principle Ulam matrix Uniformly coherent S-Space Ascent Path Analytic sets Singular Density Fast club Singular cofinality Hindman's Theorem Erdos-Hajnal graphs Generalized descriptive set theory free Souslin tree Subadditive ZFC construction very good scale Rainbow sets Subtle tree property Iterated forcing Cohen real Jonsson cardinal stick Subtle cardinal regressive Souslin tree Sakurai's Bell inequality Strongly Luzin set Coherent tree Distributive tree Reduced Power Antichain Knaster diamond star Martin's Axiom Fat stationary set Slim tree specializable Souslin tree Ineffable cardinal L-space Foundations polarized partition relation Diamond sap Nonspecial tree tensor product graph Successor of Singular Cardinal Shelah's Strong Hypothesis Whitehead Problem reflection principles Aronszajn tree weak diamond Reflecting stationary set P-Ideal Dichotomy Postprocessing function Knaster and friends Vanishing levels Local Club Condensation. countably metacompact higher Baire space square principles C-sequence Partition Relations Microscopic Approach Successor of Regular Cardinal Subnormal ideal Selective Ultrafilter Lipschitz reduction PFA(S)[S] AIM forcing super-Souslin tree approachability ideal Diamond-sharp Hedetniemi's conjecture Dowker space projective Boolean algebra Prevalent singular cardinals Singular cardinals combinatorics b-scale strongly bounded groups Parameterized proxy principle free Boolean algebra Luzin set PFA 54G20 Kurepa Hypothesis Rado's conjecture Small forcing Almost countably chromatic Almost Souslin unbounded function Erdos Cardinal Uniformly homogeneous Forcing Axioms weak square Universal Sequences Generalized Clubs coloring number Cardinal function Diamond for trees middle diamond Open Access ccc Large Cardinals Cardinal Invariants Commutative cancellative semigroups Poset xbox Prikry-type forcing Well-behaved magma Rock n' Roll Strong coloring GMA square transformations Constructible Universe Greatly Mahlo Amenable C-sequence Dushnik-Miller HOD Minimal Walks Sigma-Prikry club_AD stationary hitting Chromatic number Ramsey theory over partitions Closed coloring Axiom R
Tag Archives: free Souslin tree
Proxy principles in combinatorial set theory
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper as new foundations for the construction of $\kappa$-Souslin trees in a uniform way that does not … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged C-sequence, free Souslin tree, Parameterized proxy principle, Souslin Tree, specializable Souslin tree, square principles, xbox
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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
Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading