On the axiom of extensionality, Part II
| Autor: | R. O. Gandy |
|---|---|
| Rok vydání: | 1959 |
| Předmět: | |
| Zdroj: | Journal of Symbolic Logic. 24:287-300 |
| ISSN: | 1943-5886 0022-4812 |
| DOI: | 10.2307/2963897 |
| Popis: | In this paper it is shown that, if a certain form of Gödel-Bernays set theory which does not include the axiom of extensionality is consistent, then so is the whole system of set theory. The general line of argument is similar to that used in Part I. § 1 describes a reformulation of set theory in which the class-existence axioms are replaced by the use of abstracts. In § 2 some standard theorems, including the theory of the ancestral, are proved without using the axiom of extensionality. In § 3 the appropriate inner model is defined, and the validity in it of the most of the axioms is demonstrated. § 4 deals with the remaining axioms (of infinity and of choice). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|