On Bourbaki's axiomatic system for set theory
In this paper we study the axiomatic system proposed by Bourbaki for the Theory of Sets in the Éléments de Mathématique. We begin by examining the role played by the sign τ in the framework of its formal logical theory and then we show that the system of axioms for set theory is equivalent to Zermel...
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| Veröffentlicht in: | Synthese (Dordrecht) 2014-11, Vol.191 (17), p.4069-4098 |
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| container_title | Synthese (Dordrecht) |
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| creator | Anacona, Maribel Arboleda, Luis Carlos Pérez-Fernández, F. Javier |
| description | In this paper we study the axiomatic system proposed by Bourbaki for the Theory of Sets in the Éléments de Mathématique. We begin by examining the role played by the sign τ in the framework of its formal logical theory and then we show that the system of axioms for set theory is equivalent to Zermelo—Fraenkel system with the axiom of choice but without the axiom of foundation. Moreover, we study Grothendieck's proposal of adding to Bourbaki's system the axiom of universes for the purpose of considering the theory of categories. In this regard, we make some historical and epistemological remarks that could explain the conservative attitude of the Group. |
| doi_str_mv | 10.1007/s11229-014-0515-1 |
| format | Article |
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| subjects | Attitudes Axiom of choice Axioms Category theory Education Epistemology Logic Mathematical logic Mathematical objects Mathematical relations Mathematical set theory Mathematical sets Mathematical theorems Mathematics Metaphysics Philosophy Philosophy of Language Philosophy of Science Semiotics Set theory |
| title | On Bourbaki's axiomatic system for set theory |
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