Alternative Theories and Higher Infinite View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2013

AUTHORS

Daniel Parrochia , Pierre Neuville

ABSTRACT

We have presented in the previous chapter, a theory able to generate the infinite set of classifications as the continuum, each classification being in a one-to-one correspondence with a real number. But, as we know, there are, in the mathematics of the infinite, since the works of Cantor, Suslin and others, a lot of possible views of the continuum. Moreover, since the undecidability results of Cohen, there exist also a lot of possible set theories. So, it may be useful to ask some questions about what happens concerning the existence of classifications in those alternative theories, in particular, when they admit higher forms of the infinite. Though the risk is obvious, there, to end up at some undecidability results, several arguments speak for such an extension. More... »

PAGES

229-260

References to SciGraph publications

  • 1991. Semimodular Lattices in NONE
  • 1983-06. Lindelöf models of the reals: Solution to a problem of Sikorski in ISRAEL JOURNAL OF MATHEMATICS
  • 2009-02. Chains and antichains in partial orderings in ARCHIVE FOR MATHEMATICAL LOGIC
  • 2009-06. Mumford dendrograms and discrete p-adic symmetries in P-ADIC NUMBERS, ULTRAMETRIC ANALYSIS AND APPLICATIONS
  • 2009-12. On p-adic classification in P-ADIC NUMBERS, ULTRAMETRIC ANALYSIS AND APPLICATIONS
  • 1978. General Lattice Theory in NONE
  • 1991-09. Elementary equivalent pairs of algebras associated with sets in ALGEBRA UNIVERSALIS
  • 1985-02. Elementarily non-equivalent infinite partition lattices in ALGEBRA UNIVERSALIS
  • 2009. On a Problem of Formal Logic in CLASSIC PAPERS IN COMBINATORICS
  • Book

    TITLE

    Towards a General Theory of Classifications

    ISBN

    978-3-0348-0608-4
    978-3-0348-0609-1

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-0348-0609-1_9

    DOI

    http://dx.doi.org/10.1007/978-3-0348-0609-1_9

    DIMENSIONS

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