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