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hereditarily_finite_set [2015/08/25 22:38] nikolaj |
hereditarily_finite_set [2015/10/08 13:43] (current) nikolaj |
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===== Hereditarily finite set ===== | ===== Hereditarily finite set ===== | ||
==== Set ==== | ==== Set ==== | ||
- | | @#FFBB00: definiendum | @#FFBB00: $V_\omega$ | | + | | @#FFBB00: definiendum | @#FFBB00: $V_\omega$ in it | |
| @#55EE55: postulate | @#55EE55: $\emptyset\in V_\omega$ | | | @#55EE55: postulate | @#55EE55: $\emptyset\in V_\omega$ | | ||
| @#FFFDDD: for all | @#FFFDDD: $x\in V_\omega$ | | | @#FFFDDD: for all | @#FFFDDD: $x\in V_\omega$ | | ||
+ | | @#55EE55: postulate | @#55EE55: ${\mathcal P}(x)\in V_\omega $ | | ||
| @#55EE55: postulate | @#55EE55: $x = \emptyset\ \lor\ \exists (y\in V_\omega).\ x = {\mathcal P}(y) $ | | | @#55EE55: postulate | @#55EE55: $x = \emptyset\ \lor\ \exists (y\in V_\omega).\ x = {\mathcal P}(y) $ | | ||