## Abstract

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 language | English |
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Pages (from-to) | 53-70 |

Number of pages | 18 |

Journal | Journal of Formalized Reasoning |

Volume | 9 |

Issue number | 1 |

State | Published - 1 Jan 2016 |

Externally published | Yes |

## ASJC Scopus subject areas

- Computer Science (miscellaneous)
- General Mathematics