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