Some Basic Technical (Meta-)Mathematical Preliminaries for Cognitive Metamathematics

Danny A. J. Gómez Ramírez
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Danny A. J. Gómez Ramírez: Instituto Tecnológico Metropolitano (ITM), Research’s Labs Center Parque i

Chapter Chapter 2 in Artificial Mathematical Intelligence, 2020, pp 19-38 from Springer

Abstract: Abstract We present in a very concise manner fundamental (meta)mathematical domain-specific terminology needed for the Artificial Mathematical Intelligence program (Cognitive Metamathematics). Specifically, we briefly revise the notions of propositional and predicative logic, the most outstanding logical frameworks for modern mathematics (e.g., ZFC and NBG set theory, Peano arithmetic), and the notion of category and some of its derived notions. Moreover, a short description of fundamental algebraic, topological, and geometric notions is presented. For instance, the following notions are briefly introduced: (abelian) group, commutative ring with unity, localization, quotient ring, ideal, prime ideal, multiplicative ring, ring of polynomials in finitely many variables, field, field extension, group of automorphisms of a field (extension), (base for a) topological space, (ideal associated to a) algebraic set, ring of coordinates of an algebraic set, pre-sheaf and sheaf with values on the category of sets.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-50273-7_2

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DOI: 10.1007/978-3-030-50273-7_2

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