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This is an old suggestion of Joel David Hamkins at the end of his answer to this question: Forcing as a tool to prove theoremsForcing as a tool to prove theorems I just noticed it while trying to understand his answer. But indeed it would be nice to have a big list of $ZFC$ theorems that were proven first by forcing.

A very well known example is Silver's Theorem about the fact that the $GCH$ can't fail first at a singular cardinal of uncountable cofinality (say for instance $\aleph_{\omega_1}$), I had read somewhere (Jech, maybe) that Silver proved it first using forcing.

Also if anyone knows theorems of pcf theory that were first proven using forcing, please post them.

This is an old suggestion of Joel David Hamkins at the end of his answer to this question: Forcing as a tool to prove theorems I just noticed it while trying to understand his answer. But indeed it would be nice to have a big list of $ZFC$ theorems that were proven first by forcing.

A very well known example is Silver's Theorem about the fact that the $GCH$ can't fail first at a singular cardinal of uncountable cofinality (say for instance $\aleph_{\omega_1}$), I had read somewhere (Jech, maybe) that Silver proved it first using forcing.

Also if anyone knows theorems of pcf theory that were first proven using forcing, please post them.

This is an old suggestion of Joel David Hamkins at the end of his answer to this question: Forcing as a tool to prove theorems I just noticed it while trying to understand his answer. But indeed it would be nice to have a big list of $ZFC$ theorems that were proven first by forcing.

A very well known example is Silver's Theorem about the fact that the $GCH$ can't fail first at a singular cardinal of uncountable cofinality (say for instance $\aleph_{\omega_1}$), I had read somewhere (Jech, maybe) that Silver proved it first using forcing.

Also if anyone knows theorems of pcf theory that were first proven using forcing, please post them.

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Examples of ZFC theorems proved via forcing

This is an old suggestion of Joel David Hamkins at the end of his answer to this question: Forcing as a tool to prove theorems I just noticed it while trying to understand his answer. But indeed it would be nice to have a big list of $ZFC$ theorems that were proven first by forcing.

A very well known example is Silver's Theorem about the fact that the $GCH$ can't fail first at a singular cardinal of uncountable cofinality (say for instance $\aleph_{\omega_1}$), I had read somewhere (Jech, maybe) that Silver proved it first using forcing.

Also if anyone knows theorems of pcf theory that were first proven using forcing, please post them.