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