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> he said that according to L-S theorem there are countable sets that are models of set theory (ZFC to be precise). This is not really true since it contradicts Goedel's incompleteness theorem

Could you clarify this a bit? I think Scott's very open to suggestions and corrections

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I should have said that one cannot prove this in ZFC (of course there may be models of ZFC in which this is true) since that would meant one can prove Con ZFC in ZFC. Mostowski's theorems however are provable in ZFC and are enough for the arithmetic proofs that are produced by the method of forcing.

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