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\(\mu\)-Abstract Elementary Classes and other generalizations

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      Abstract

      We introduce \(\mu\)-Abstract Elementary Classes (\(\mu\)-AECs) as a broad framework for model theory that includes complete boolean algebras and Dirichlet series, and begin to develop their classification theory. Moreover, we note that \(\mu\)-AECs correspond precisely to accessible categories in which all morphisms are monomorphisms, and begin the process of reconciling these divergent perspectives: not least, the preliminary classification-theoretic results for {\mu}-AECs transfer directly to accessible categories with monomorphisms.

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      Journal
      2015-09-24
      2016-02-11
      1509.07377
      10.1016/j.jpaa.2016.02.002

      http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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      03C48 (Primary), 03C45, 18C35, 03C52, 03C55, 03C75, 03E55 (Secondary)
      Journal of Pure and Applied Algebra 220 (2016), no. 9, 3048-3066
      26 pp
      math.LO math.CT

      General mathematics, Logic & Foundation

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