Full Idea
A consistent theory is, by definition, one satisfied by some model; an isomorphic image of a model satisfies the same theories as the original model; to provide the making of an isomorphic image of any given model, a domain need only be large enough.
Gist of Idea
A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those
Source
David Lewis (Putnam's Paradox [1984], 'Why Model')
Book Reference
Lewis,David: 'Papers in Metaphysics and Epistemology' [CUP 1999], p.68
A Reaction
This is laying out the ground for Putnam's model theory argument in favour of anti-realism. If you are chasing the one true model of reality, then formal model theory doesn't seem to offer much encouragement.
Related Idea
Idea 14207 If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth [Putnam]