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A Logical Framework for Developing and Mechanizing Set Theories

Conference paper
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 9706)

Abstract

We describe a framework for formalizing mathematics which is based on the usual set theoretical foundations of mathematics. Its most important feature is that it reflects real mathematical practice in making an extensive use of statically defined abstract set terms, in the same way they are used in ordinary mathematical discourse. We also show how large portions of scientifically applicable mathematics can be developed in this framework in a straightforward way, using just rather weak set theories which are predicatively acceptable. The key property of those theories is that every object which is used in it is defined by some closed term of the theory. This allows for a very concrete, computationally-oriented interpretation. However, the development is not committed to such interpretation, and can easily be extended for handling stronger set theories, including ZFC itself.

Keywords

Ordinary Mathematical Discourse Actual Mathematical Practice Predicative Theories Rudimentary Functions Mathematical Knowledge Management (MKM) 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Computer ScienceTel Aviv UniversityTel AvivIsrael

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