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Variations on a theme by Ishihara

  • HANNES DIENER (a1)
Abstract

Ishihara's tricks have proven to be a highly useful tool in constructive mathematics, since they enable one to make decisions that seem, on first glance, impossible. They do, however, require that one deals with strongly extensional mappings on complete spaces. In this short note, we show how these assumptions can be weakened. Furthermore, we apply these generalizations to give a partial answer to the question, whether constructively we can rule out the existence of injections from Baire space into the natural numbers, to a version of Riemann's per mutation theorem and to a classification problem about cardinalities in constructive reverse mathematics.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

E. Bishop and D. Bridges (1985) Constructive Analysis, Springer-Verlag.

D. S. Bridges and L. S. Vîţă (2006) Techniques of Constructive Analysis, Universitext. Springer, New York, 2006.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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