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Reflecting stationary set Knaster and friends Fast club stick Almost Souslin Local Club Condensation. C-sequence Forcing Axioms unbounded function square principles PFA stationary hitting Souslin Tree Strong coloring Dowker space Jonsson cardinal Parameterized proxy principle Strongly Luzin set Well-behaved magma very good scale Iterated forcing Slim tree L-space Small forcing positive partition relation free Boolean algebra Mandelbrot set Subtle cardinal full tree Fat stationary set Sakurai's Bell inequality Universal Sequences Prikry-type forcing Intersection model square Entangled linear order Strongly compact cardinal approachability ideal HOD Vanishing levels Uniformly homogeneous Shelah's Strong Hypothesis Almost-disjoint family Singular Density Commutative projection system Square-Brackets Partition Relations nonmeager set xbox O-space Coherent tree Precaliber weak square Luzin set Cardinal function Respecting tree Prevalent singular cardinals Generalized descriptive set theory higher Baire space Subtle tree property Chromatic number middle diamond Successor of Regular Cardinal incompactness Diamond for trees Sierpinski's onto mapping principle reflection principles tensor product graph Hedetniemi's conjecture Microscopic Approach Minimal Walks Ulam matrix coloring number PFA(S)[S] Rainbow sets Knaster Martin's Axiom Uniformly coherent projective Boolean algebra Ascent Path strongly bounded groups P-Ideal Dichotomy sap perfectly normal Kurepa Hypothesis polarized partition relation Singular cofinality Cardinal Invariants S-Space Foundations Commutative cancellative semigroups Non-saturation Antichain transformations Large Cardinals Aronszajn tree weak Kurepa tree Generalized Clubs Distributive tree Poset Dushnik-Miller Subadditive Lipschitz reduction diamond star indecomposable filter Monotonically far Hindman's Theorem Singular cardinals combinatorics Hereditarily Lindelöf space Rock n' Roll countably metacompact Nonspecial tree Analytic sets Ostaszewski square free Souslin tree Whitehead Problem Chang's conjecture super-Souslin tree Open Access club_AD Was Ulam right? Erdos Cardinal Rado's conjecture Fodor-type reflection ccc Sigma-Prikry Partition Relations stationary reflection Ineffable cardinal SNR Cohen real Postprocessing function Diamond Club Guessing Uniformization GMA Ascending path Constructible Universe Countryman line Reduced Power Erdos-Hajnal graphs Forcing with side conditions Successor of Singular Cardinal OCA regressive Souslin tree specializable Souslin tree weak diamond ZFC construction Forcing Amenable C-sequence Absoluteness Partition relations for trees AIM forcing Interval topology on trees Axiom R Weakly compact cardinal Almost countably chromatic Diamond-sharp Closed coloring Filter reflection 54G20 Ramsey theory over partitions Greatly Mahlo Selective Ultrafilter Subnormal ideal b-scale
Tag Archives: Shelah’s Strong Hypothesis
Logic in Hungary, August 2005
These are the slides of a contributed talk given at the Logic in Hungary 2005 meeting (Budapest, 5–11 August 2005). Talk Title: On the consistency strength of the Milner-Sauer Conjecture Abstract: In their paper from 1981, after learning about Pouzet‘s theorem that any … Continue reading
Posted in Contributed Talks
Tagged Antichain, Shelah's Strong Hypothesis, Singular cofinality
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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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The failure of diamond on a reflecting stationary set
Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … 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
