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