A logical framework for developing and mechanizing set theories

Arnon Avron*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationAutomated Reasoning - 8th International Joint Conference, IJCAR 2016, Proceedings
EditorsNicola Olivetti, Ashish Tiwari
PublisherSpringer Verlag
Number of pages6
ISBN (Print)9783319402284
StatePublished - 2016
Event8th International Joint Conference on Automated Reasoning, IJCAR 2016 - Coimbra, Portugal
Duration: 27 Jun 20162 Jul 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th International Joint Conference on Automated Reasoning, IJCAR 2016


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