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This tag is for questions about proving that some statement is independent from a theory, meaning it is neither provable nor refutable from that theory. Common examples are the continuum hypothesis from the axioms of ZFC, and the axiom of choice from the axioms of ZF.

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Why can we assume a ctm of ZFC exists in forcing

This is to slightly elaborate on point 2 of Noah Schweiber's answer, since in my opinion this approach is often presented in a somewhat confusing manner which ommits some key subtelties. Forcing const …
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