I'm interested in books and/or articles which explore a little more in depth the model theory of set theory. I'm aware that most books on set theory have a section or two on models (e.g. Jech, Kunen), but these sections are generally redacted with a certain instrumental aim in mind. I'm more interested in books or articles that tackle the model theory for set theory head on; for instance, there seems to be a distinction between models and interpretations of set theory, yet most books don't examine that. In the same vein, it seems (correct me if I'm wrong) that, assuming ZFC is consistent, we can, as per the completeness theorem, also assume that it has a model. Yet we can't assume that this model is a standard transitive model, for then the theory would prove an inconsistency. If true, it'd be nice to see this fleshed out in a bit more detail.
2026-03-29 15:14:47.1774797287
Books and articles on model theory for set theory
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