| Автор | Heidema, Johannes |
| Дата выпуска | 1990 |
| dc.description | Unrestricted use of the axiom schema of comprehension, ‘to every mathematically (or set-theoretically) describable property there corresponds the set of all mathematical (or set-theoretical) objects having that property’, leads to contradiction. In set theories of the Zermelo–Fraenkel–Skolem (ZFS) style suitable instances of the comprehension schema are chosen ad hoc as axioms, e.g.axioms which guarantee the existence of unions, intersections, pairs, subsets, empty set, power sets and replacement sets. It is demonstrated that a uniform syntactic description may be given of acceptable instances of the comprehension schema, which include all of the axioms mentioned, and which in their turn are theorems of the usual versions of ZFS set theory.Well then, shall we proceed as usual and begin by assuming the existence of a single essential nature or Form for every set of things which we call by the same name? Do you understand?(Plato, Republic X.596a6; cf. Cornford 1966, 317) |
| Формат | application.pdf |
| Издатель | Taylor & Francis |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Название | An axiom schema of comprehension of zermelo–fraenkel–skolem set theory |
| Тип | research-article |
| DOI | 10.1080/01445349008837157 |
| Electronic ISSN | 1464-5149 |
| Print ISSN | 0144-5340 |
| Журнал | History and Philosophy of Logic |
| Том | 11 |
| Первая страница | 59 |
| Последняя страница | 65 |
| Аффилиация | Heidema, Johannes; Department of Mathematics, Rand Afrikaans University |
| Выпуск | 1 |
| Библиографическая ссылка | Cornford, F. M . 1966. The Republic of Plato, Oxford: Clarendon Press. |
| Библиографическая ссылка | Dauben, J. W. 1988. Cantorian set theory and limitations of size. British journal for the philosophy of science, 39: 541–550. (review of Hallett 1984) |
| Библиографическая ссылка | Fraenkel, A. A., Bar-Hillel, Y., Levy, A. and Van Dalen, D. 1973. Foundations of set theory, 2nd, Amsterdam: North-Holland. |
| Библиографическая ссылка | Hallett, M. 1984. Cantorian set theory and limitation of size, Oxford: Clarendon Press. |
| Библиографическая ссылка | Levy, A. Parameters in comprehension axiom schemas of set theory. Proceedings of the Tarski symposium. Netherlands. Edited by: Henkin, L. pp.309–324. Rhode Island et Providence, alii |
| Библиографическая ссылка | Quine, W. and Van, O. 1969. Set theory and its logic, Cambridge, Massachusetts: Belknap Press. |
| Библиографическая ссылка | Shoenfield, J. R. 1977. “Axioms of set theory”. In Handbook of mathematical logic, Edited by: Barwise, J. 321–344. Amsterdam: North-Holland. |
| Библиографическая ссылка | Wang, H. 1974. From mathematics to philosophy, London: Routledge and Kegan Paul. |
