In the context of the Löwenheim–Skolem theorem and "Skolem's Paradox", what does it mean for 'the domain of a model to be countable'?
My only guess is that the number of 'objects and/or relations' in the model forms a set of countable size.
Contrast this with the size of the objects in the model. e.g., if you have a set of countably infinite cardinality where the elements might be sets of uncountably infinite size.
My only guess is that the number of 'objects and/or relations' in the model forms a set of countable size.
Contrast this with the size of the objects in the model. e.g., if you have a set of countably infinite cardinality where the elements might be sets of uncountably infinite size.