AN EXTENSION OF A THEOREM OF ZERMELO
We show that if (M, ∈1, ∈2) satisfies the first-order Zermelo–Fraenkel axioms of set theory when the membership relation is ∈1 and also when the membership relation is ∈2, and in both cases the formulas are allowed to contain both ∈1 and ∈2, then (M, ∈1) ≅ (M, ∈2), and the isomorphism is definable i...
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| Veröffentlicht in: | The bulletin of symbolic logic 2019-06, Vol.25 (2), p.208-212 |
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| creator | VÄÄNÄNEN, JOUKO |
| description | We show that if (M, ∈1, ∈2) satisfies the first-order Zermelo–Fraenkel axioms of set theory when the membership relation is ∈1 and also when the membership relation is ∈2, and in both cases the formulas are allowed to contain both ∈1 and ∈2, then (M, ∈1) ≅ (M, ∈2), and the isomorphism is definable in (M, ∈1, ∈2). This extends Zermelo's 1930 theorem in [6]. |
| doi_str_mv | 10.1017/bsl.2019.15 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 1079-8986 |
| ispartof | The bulletin of symbolic logic, 2019-06, Vol.25 (2), p.208-212 |
| issn | 1079-8986 1943-5894 |
| language | eng |
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| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy; Cambridge University Press Journals Complete |
| subjects | Axioms Categoricity Communications First order theories Hypotheses Isomorphism Logical theorems Mathematical logic Mathematical relations Mathematical set theory Mathematical theorems Set theory Symmetry Theorems Zermelo Frankel set theory |
| title | AN EXTENSION OF A THEOREM OF ZERMELO |
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