WHY TOPOLOGY IN THE MINIMALIST FOUNDATION MUST BE POINTFREE.

We give arguments explaining why, when adopting a minimalist approach to constructive mathematics as that formalized in our two-level minimalist foundation, the choice for a pointfree approach to topology is not just a matter of convenience or mathematical elegance, but becomes compulsory. The main...

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Publicado en:Logic & Logical Philosophy Vol. 22; no. 2; pp. 167 - 200
Autores principales: Maietti, Maria Emilia, Sambin, Giovanni
Formato: Artículo
Publicado: Logic & Logical Philosophy Jun2013
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Acceso en línea:Ver este registro en EBSCOhost
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          Maietti, Maria Emilia
          Sambin, Giovanni
        affil: Dipartimento di Matematica, Università di Padova, via Trieste 63 35121 Padova, Italy
      su:
        Mathematical programming
        Mathematics
        Topology
        Real numbers
        Axioms
      sug:
        subj:
          Mathematical programming
          Mathematics
          Topology
          Real numbers
          Axioms
      keyword:
        axiom of unique choice
        Bar Induction
        choice sequences
        constructive type theory
        minimalist foundation
        pointfree topology
        real numbers
      ab: We give arguments explaining why, when adopting a minimalist approach to constructive mathematics as that formalized in our two-level minimalist foundation, the choice for a pointfree approach to topology is not just a matter of convenience or mathematical elegance, but becomes compulsory. The main reason is that in our foundation real numbers, either as Dedekind cuts or as Cauchy sequences, do not form a set.
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