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Non-saturation Minimal Walks free Boolean algebra Prevalent singular cardinals Countryman line Precaliber Fat stationary set 54G20 Ascent Path Subadditive weak diamond weak square Strong coloring approachability ideal Cardinal Invariants Ostaszewski square unbounded function Square-Brackets Partition Relations Subtle cardinal Subnormal ideal projective Boolean algebra Hereditarily Lindelöf space Closed coloring Partition relations for trees Knaster Generalized descriptive set theory Was Ulam right? Forcing with side conditions Singular Density Iterated forcing countably metacompact Rado's conjecture C-sequence Successor of Singular Cardinal GMA Sigma-Prikry very good scale super-Souslin tree Intersection model ZFC construction Dushnik-Miller Successor of Regular Cardinal Hindman's Theorem Sakurai's Bell inequality Almost countably chromatic Diamond HOD Distributive tree Monotonically far Souslin Tree Antichain indecomposable filter Chang's conjecture Club Guessing Commutative cancellative semigroups Vanishing levels Forcing Fast club PFA(S)[S] Open Access polarized partition relation Almost Souslin stationary hitting Filter reflection Fodor-type reflection P-Ideal Dichotomy Weakly compact cardinal Hedetniemi's conjecture Strongly Luzin set Uniformization Nonspecial tree Chromatic number Luzin set Slim tree stationary reflection Rock n' Roll OCA Ineffable cardinal Parameterized proxy principle square Ulam matrix incompactness xbox Generalized Clubs Cohen real Greatly Mahlo Whitehead Problem strongly bounded groups coloring number Cardinal function O-space Uniformly coherent Analytic sets ccc Diamond-sharp Poset nonmeager set diamond star Rainbow sets Lipschitz reduction tensor product graph PFA full tree Strongly compact cardinal club_AD Microscopic Approach Large Cardinals perfectly normal Reduced Power reflection principles Knaster and friends square principles SNR Almost-disjoint family Partition Relations Singular cardinals combinatorics Absoluteness Singular cofinality free Souslin tree Uniformly homogeneous middle diamond stick sap Subtle tree property L-space Coherent tree Axiom R weak Kurepa tree Shelah's Strong Hypothesis Jonsson cardinal Entangled linear order Forcing Axioms transformations higher Baire space Selective Ultrafilter Erdos-Hajnal graphs Sierpinski's onto mapping principle Kurepa Hypothesis Postprocessing function AIM forcing S-Space Interval topology on trees Amenable C-sequence specializable Souslin tree Dowker space Local Club Condensation. Aronszajn tree Well-behaved magma Small forcing Ascending path Reflecting stationary set Martin's Axiom positive partition relation Erdos Cardinal Diamond for trees b-scale Mandelbrot set Commutative projection system Universal Sequences regressive Souslin tree Prikry-type forcing Constructible Universe Ramsey theory over partitions Foundations Respecting tree
Tag Archives: 05C05
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
A microscopic approach to Souslin-tree constructions. Part I
Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
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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
