5 ms·
I am looking forward to the next part but he has already said something that will be a a problem later on: he said that according to L-S theorem there are count
by zzless 6y ago
I am looking forward to the next part but he has already said something that will be a a problem later on: 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. What the method of forcing uses, however, is a pair of theorems by Mostowski: the reflection and the collapse theorem that let one find a model of any finite(ly axiomatizable) portion of ZFC. Finite axiomatizations of set theory (say, GB) have similar tricks. His intuition is right on though.
- Recursing 6y ago> 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
- zzless 6y agoI 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.