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tensor product graph Large Cardinals Fast club coloring number Diamond Precaliber Rainbow sets HOD Local Club Condensation. Prikry-type forcing Constructible Universe Ascending path Strong coloring square Amenable C-sequence Reduced Power Ascent Path Vanishing levels Respecting tree Partition Relations Ineffable cardinal club_AD AIM forcing Jonsson cardinal perfectly normal projective Boolean algebra Sakurai's Bell inequality super-Souslin tree Axiom R Was Ulam right? Luzin set Square-Brackets Partition Relations Forcing with side conditions Reflecting stationary set Distributive tree Club Guessing approachability ideal Generalized Clubs Strongly compact cardinal Parameterized proxy principle Dushnik-Miller Chang's conjecture polarized partition relation S-Space specializable Souslin tree indecomposable filter sap Shelah's Strong Hypothesis Small forcing Entangled linear order Ostaszewski square Hereditarily Lindelöf space Antichain Ramsey theory over partitions PFA Fat stationary set Prevalent singular cardinals Uniformization Singular Density Subtle tree property Filter reflection Cardinal function Knaster and friends Generalized descriptive set theory Lipschitz reduction O-space Ulam matrix Nonspecial tree Hindman's Theorem Greatly Mahlo square principles countably metacompact L-space Well-behaved magma Kurepa Hypothesis Subnormal ideal Cohen real Erdos Cardinal Dowker space Rock n' Roll b-scale positive partition relation Weakly compact cardinal Successor of Singular Cardinal Souslin Tree 54G20 free Souslin tree Fodor-type reflection Uniformly coherent weak square Interval topology on trees ZFC construction stationary reflection Hedetniemi's conjecture Singular cofinality C-sequence Sigma-Prikry Cardinal Invariants xbox Selective Ultrafilter Countryman line incompactness OCA Aronszajn tree Commutative projection system Singular cardinals combinatorics Subtle cardinal Forcing Poset Chromatic number GMA Martin's Axiom stick SNR weak Kurepa tree Successor of Regular Cardinal Diamond for trees Partition relations for trees Coherent tree Closed coloring nonmeager set Slim tree Almost Souslin Almost countably chromatic Mandelbrot set Postprocessing function Diamond-sharp Microscopic Approach middle diamond Knaster transformations Uniformly homogeneous unbounded function Universal Sequences Rado's conjecture reflection principles Foundations full tree ccc Open Access strongly bounded groups Minimal Walks Non-saturation weak diamond free Boolean algebra diamond star regressive Souslin tree Erdos-Hajnal graphs PFA(S)[S] Iterated forcing Strongly Luzin set Whitehead Problem higher Baire space Monotonically far P-Ideal Dichotomy Forcing Axioms very good scale Subadditive Intersection model Analytic sets stationary hitting Absoluteness Almost-disjoint family Sierpinski's onto mapping principle Commutative cancellative semigroups
Tag Archives: 03E65
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
A topological reflection principle equivalent to Shelah’s strong hypothesis
Abstract: We notice that Shelah’s Strong Hypothesis (SSH) is equivalent to the following reflection principle: Suppose $\mathbb X$ is an (infinite) first-countable space whose density is a regular cardinal, $\kappa$. If every separable subspace of $\mathbb X$ is of cardinality at most … Continue reading
Posted in Compactness, Publications, Topology
Tagged 03E04, 03E65, 54G15, Open Access, Shelah's Strong Hypothesis
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Openly generated Boolean algebras and the Fodor-type reflection principle
Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading
Posted in Compactness, Publications
Tagged 03E35, 03E55, 03E65, 03E75, 03G05, 06E05, Axiom R, Fodor-type reflection, free Boolean algebra, projective Boolean algebra, Shelah's Strong Hypothesis, stationary reflection
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On guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading
On the consistency strength of the Milner-Sauer conjecture
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading
