A Calibration of Ineffective Theorems of Analysis in a Hierarchy of Semi-classical Logical Principles

  • Michael Toftdal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)


We classify a number of nonconstructive mathematical theorems by means of a hierarchy of logical principles which are not included in intuitionistic logic. The main motivation is the development of the logical hierarchy by Akama Y. et al. and its connection to the so-called limit computable mathematics and proof animations developed by Hayashi S. et al. The results presented give insights in both the scope of limit computable mathematics and its subsystems, and the nature of the theorems of classical mathematics considered.


Limit Point Cauchy Sequence Bounded Variation Classical Logic Computable Function 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Michael Toftdal
    • 1
  1. 1.Department of Computer ScienceUniversity of AarhusAarhus NDenmark

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