Talk:Absoluteness (logic)
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About the Failure of absoluteness for countability: It is not possible to cook a counterexample for the absoluteness of countability using the Löwenheim-Skolem theorem as this produces elementary submodels (hence every formula is absolute between these models). For fixing this, after obtaining an elementary submodel of ZFC (or some H(\theta)) you use the Mostowski collapse lemma to obtain a countable transitive model M of ZFC. If x is the object that M thinks is the set of real numbers, then, using the fact that x is a subset of M (this will fail if M is an elementary submodel of H(\theta)), x is countable in H(\theta). I think the whole section of this article should be rewritten as it contains misleading information. 177.243.8.152 (talk) 05:19, 1 April 2015 (UTC)