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2018 •
We prove that several definitions of superstability in abstract elementary classes (AECs) are equivalent under the assumption that the class is stable, tame, has amalgamation, joint embedding, and arbitrarily large models. This partially answers questions of Shelah. <strong>Theorem 0.1</strong>. Let K be a tame AEC with amalgamation, joint embedding, and arbitrarily large models. Assume K is stable. Then the following are equivalent: (1) For all high-enough λ, there exists κ ≤ λ such that there is a good λ-frame on the class of κ-saturated models in Kλ. (2) For all high-enough λ, K has a unique limit model of cardinality λ. (3) For all high-enough λ, K has a superlimit model of cardinality λ. (4) For all high-enough λ, the union of a chain of λ-saturated models is λ-saturated. (5) There exists θ such that for all high-enough λ, K is (λ, θ)- solvable.
Mathematical Logic Quarterly
Around independence and domination in metric abstract elementary classes: assuming uniqueness of limit models2014 •
"We study versions of limit models adapted to the context of metric abstract elementary classes. Under superstability-like assumptions, we prove some generalizations of theorems from [GrVaVi]. We prove criteria for existence and uniqueness of limit models in the metric context."
2016 •
Starting from an abstract elementary class with no maximal models, Shelah and Villaveces have shown (assuming instances of diamond) that categoricity implies a superstability-like property for a certain independence relation called nonsplitting. We generalize their result as follows: given an abstract notion of independence for Galois (orbital) types over models, we derive that the notion satisfies a superstability property provided that the class is categorical and satisfies a weakening of amalgamation. This extends the Shelah-Villaveces result (the independence notion there was splitting) as well as a result of the first and second author where the independence notion was coheir. The argument is in ZFC and fills a gap in the Shelah-Villaveces proof.
The Journal of Symbolic Logic
Equivalent Definitions of Superstability in Tame Abstract Elementary ClassesIn the context of abstract elementary classes (AECs) with a monster model, several possible definitions of superstability have appeared in the literature. Among them are no long splitting chains, uniqueness of limit models, and solvability. Under the assumption that the class is tame and stable, we show that (asymptotically) no long splitting chains implies solvability and uniqueness of limit models implies no long splitting chains. Using known implications, we can then conclude that all the previously-mentioned definitions (and more) are equivalent:Corollary.LetKbe a tame AEC with a monster model. Assume thatKis stable in a proper class of cardinals. The following are equivalent:(1)For all high-enough λ,Khas no long splitting chains.(2)For all high-enough λ, there exists a good λ-frame on a skeleton ofKλ.(3)For all high-enough λ,Khas a unique limit model of cardinality λ.(4)For all high-enough λ,Khas a superlimit model of cardinality λ.(5)For all high-enough λ, the union of any inc...
We introduce µ-Abstract Elementary Classes (µ-AECs) as a broad framework for model theory that includes complete boolean algebras and metric spaces, and begin to develop their classification theory. Moreover, we note that µ-AECs correspond precisely to accessible categories in which all morphisms are monomorphisms, and begin the process of reconciling these divergent perspectives: for example, the preliminary classification-theoretic results for µ-AECs transfer directly to accessible categories with monomorphisms.
2005 •
A topos version of Cantor’s back and forth theorem is established and used to prove that the ordered structure of the rational numbers 〈Q, <〉 is homogeneous in any topos with natural numbers object. The notion of effective homogeneity is introduced, and it is shown that 〈Q, <〉 is a minimal effectively homogeneous structure, that is, it can be embedded in every other effectively homogeneous ordered structure.
Academia Green Energy
A study of the calorific power of corncob briquettes, using residual oils as binders2024 •
La Fuerza Constituyente Inicial
La Fuerza Constituyente Inicial - Tulio Álvarez (2)2011 •
dos mi diecisiete
LOS SISTEMAS DE INFORMACIÓN CONTABLE Y SU RELACIÓN CON LAS HERRAMIENTAS TECNOLÓGICAS2017 •
Economic Approaches to Organizations, 5th edition, chapter 13
Economic approaches to mergers and acquisitions (PDF)2013 •
2024 •
Prehospital and Disaster Medicine
Keeping our Healthcare Workers Safe–Ebola and COVID-19Michigan Mathematical Journal
Equivariant elliptic homology and finite groups1996 •
2018 IEEE Applied Power Electronics Conference and Exposition (APEC)
High efficiency Capacitive Power Transfer Converter2018 •
Medical Physics
Tomographic mammography using a limited number of low‐dose cone‐beam projection images2003 •
Journal of the Acoustical Society of America
Laboratory and clinical use of the electroglottograph1993 •
Molecular Genetics & Genomic Medicine
Mutations in the PH Domain of <i>DNM1</i> are associated with a nonepileptic phenotype characterized by developmental delay and neurobehavioral abnormalities2018 •
Global Change Biology
Elevated ozone reduces methane emissions from peatland mesocosms2010 •
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Fusion of cleavage site detection and pairwise alignment for fast subcellular localization2008 •