Leibnizian models of set theory
نویسنده
چکیده
A model is said to be Leibnizian if it has no pair of indiscernibles. Mycielski has shown that there is a first order axiom LM (the LeibnizMycielski axiom) such that for any completion T of Zermelo-Fraenkel set theory ZF , T has a Leibnizian model iff T proves LM. Here we prove: Theorem A. Every complete theory T extending ZF + LM has 2 א 0 nonisomorphic countable Leibnizian models. Theorem B. If κ is a prescribed definable infinite cardinal of a complete theory T extending ZF+ V =OD, then there are 2 א 1
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ورودعنوان ژورنال:
- J. Symb. Log.
دوره 69 شماره
صفحات -
تاریخ انتشار 2004