Skip to main content
    • Aa
    • Aa

Variations on a theme by Ishihara


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.

Linked references
Hide All

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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 12 *
Loading metrics...

Abstract views

Total abstract views: 75 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd June 2017. This data will be updated every 24 hours.