Banishing Ultrafilters from Our Consciousness

  • Domenico CantoneEmail author
  • Eugenio G. Omodeo
  • Alberto Policriti
Part of the Outstanding Contributions to Logic book series (OCTR, volume 10)


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 



Discussions with Francesco Di Cosmo helped in polishing this paper. The first author acknowledges partial support from the Polish National Science Centre research project DEC-2011/02/A/HS1/00395; and the second author from the project FRA-UniTS (2014) “Learning specifications and robustness in signal analysis.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Domenico Cantone
    • 1
    Email author
  • 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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