### Abstract

Original language | Undefined |
---|---|

Title of host publication | Reflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday |

Editors | E. Barendsen, V. Capretta, H. Geuvers, M. Niqui |

Place of Publication | Nijmegen |

Publisher | Radboud University |

Pages | 223-232 |

Number of pages | 14 |

ISBN (Print) | 978-90-9022446-6 |

Publication status | Published - 17 Dec 2007 |

### Publication series

Name | |
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Publisher | Radboud University |

Number | Supplement |

### Keywords

- IR-64509
- EWI-11511
- METIS-245832

### Cite this

*Reflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday*(pp. 223-232). Nijmegen: Radboud University.

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*Reflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday.*Radboud University, Nijmegen, pp. 223-232.

**Binary Relations as a Foundation of Mathematics.** / Kuper, Jan.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

TY - CHAP

T1 - Binary Relations as a Foundation of Mathematics

AU - Kuper, Jan

PY - 2007/12/17

Y1 - 2007/12/17

N2 - We describe a theory for binary relations in the Zermelo-Fraenkel style. We choose for ZFCU, a variant of ZFC Set theory in which the Axiom of Foundation is replaced by an axiom allowing for non-wellfounded sets. The theory of binary relations is shown to be equi-consistent ZFCU by constructing a model for the theory of binary relations in ZFU and vice versa. Thus, binary relations are a foundation for mathematics in the same sense as sets are.

AB - We describe a theory for binary relations in the Zermelo-Fraenkel style. We choose for ZFCU, a variant of ZFC Set theory in which the Axiom of Foundation is replaced by an axiom allowing for non-wellfounded sets. The theory of binary relations is shown to be equi-consistent ZFCU by constructing a model for the theory of binary relations in ZFU and vice versa. Thus, binary relations are a foundation for mathematics in the same sense as sets are.

KW - IR-64509

KW - EWI-11511

KW - METIS-245832

M3 - Chapter

SN - 978-90-9022446-6

SP - 223

EP - 232

BT - Reflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday

A2 - Barendsen, E.

A2 - Capretta, V.

A2 - Geuvers, H.

A2 - Niqui, M.

PB - Radboud University

CY - Nijmegen

ER -