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