Formalizing scientifically applicable mathematics in a definitional framework

Arnon Avron, Liron Cohen

Research output: Contribution to journalArticlepeer-review


In [3] a new framework for formalizing mathematics was developed. The main new features of this framework are that it is based on the usual first-order set theoretical foundations of mathematics (in particular, it is type-free), but it reflects real mathematical practice in making an extensive use of statically defined abstract set terms of the form (x | φ), in the same way they are used in ordinary mathematical discourse. In this paper we show how large portions of fundamental, scientifically applicable mathematics can be developed in this framework in a straightforward way, using just a rather weak set theory which is predicatively acceptable and essentially first-order. The key property of that theory 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 of the theory. However, the development is not committed to such interpretation, and can easily be extended for handling stronger set theories (including ZF).

Original languageEnglish
Pages (from-to)53-70
Number of pages18
JournalJournal of Formalized Reasoning
Issue number1
StatePublished - 2016


FundersFunder number
Ministry of Science and Technology, Israel


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