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