Leibnizian models of set theory
Abstract.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 Leibniz-Mycielski axiom) such that for any completion T of Zermelo-Fraenkel set theory ZF. T has a Leibnizian model if and only if T proves LM. Here we prove:Theorem A. Every complete theory T extending ZF + LM has nonisomorphic countable Leibnizian models.Theorem B. If κ is a prescribed definable infinite cardinal ofa complete theory T extending ZF + V = OD, then there are nonisomorphic Leibnizian models of T of power ℵ1such thatis ℵ1-like.Theorem C. Every complete theory T extendingZF + V = ODhas nonisomorphic ℵ1-like Leibnizian models.
1987 ◽
Vol 30
(4)
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pp. 385-392
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2018 ◽
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2003 ◽
Vol 120
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pp. 225-236
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2000 ◽
Vol 39
(7)
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pp. 509-514
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