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