There are also some model-theoretic examples of such proofs (in ZFC). Once you prove that for a given logic L, the notions of consistency and completeness (for theories in L) are absolute, it's possible to prove (in ZFC) the existence of some interesting models (described by an L-theory) just by showing that such models exist in some generic extension. One example is presented in a paper by Shelah called "Nonstandard uniserial module over a uniserial domain exists", the proof uses a completeness theorem for stationary logic.
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There are also some model-theoretic examples of such proofs (in ZFC). Once you prove that for a given logic L, the notions of consistency and completeness (for theories in L) are absolute, it's possible to prove (in ZFC) the existence of some interesting models (described by an L-theory) just by showing that such models exist in some generic extension. One example is presented in a paper by Shelah called "Nonstandard uniserial module over a uniserial domain exists". |
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