Banishing Ultrafilters from Our Consciousness

  • Domenico Cantone
  • Eugenio G. Omodeo
  • Alberto Policriti


The way in which Martin Davis conceived the first chapter of his book “Applied nonstandard analysis ” is a brilliant example of information hiding as a guiding principle for the design of widely applicable constructions and methods of proof. We discuss here a common trait that we see between that book and another writing of the year 1977, “Metamathematical extensibility for theorem provers and proof-checkers”, which Martin coauthored with Jacob T. Schwartz. To tie the said part of Martin’s study on nonstandard analysis to proof technology, we undertake a verification, by means of a proof-checker based on set theory, of key results of the non-standard approach to analysis.


Proof checking Proof engineering Nonstandard analysis Foundations of infinitesimal calculus 

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Domenico Cantone
    • 1
  • Eugenio G. Omodeo
    • 2
  • Alberto Policriti
    • 3
  1. 1.DMI, Università di CataniaCataniaItaly
  2. 2.DMG/DMI, Università di TriesteTriesteItaly
  3. 3.DMIF, Università di UdineUdineItaly

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