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There are statements which are independent but not provably independent

If the independence of a statement is a meta-mathematical theorem, then the existence of statements which are independent but not provably independent is a meta-meta-mathematical theorem.
See the post: Are there statements that are undecidable but not provably undecidable (undecidable is here synonymous of independent) and the positive answer (under ZFC, assuming its consistence).

There are statements which are independent but not provably independent

If the independence of a statement is a meta-mathematical theorem, then the existence of statements which are independent but not provably independent is a meta-meta-mathematical theorem.
See the post: Are there statements that are undecidable but not provably undecidable (undecidable is here synonymous of independent) and the positive answer (under ZFC, assuming its consistence).

There are statements which are independent but not provably independent

If the independece of a statement is a meta-mathematical theorem, then the existence of statements which are independent and non provably independent is a meta-meta-mathematical theorem.
See the post: Are there statements that are undecidable but not provably undecidable (undecidable is here synonymous of independent) and the positive answer under ZFC (assuming its consistence).

There are statements which are independent but not provably independent

If the independence of a statement is a meta-mathematical theorem, then the existence of statements which are independent but not provably independent is a meta-meta-mathematical theorem.
See the post: Are there statements that are undecidable but not provably undecidable (undecidable is here synonymous of independent) and the positive answer (under ZFC, assuming its consistence).

There are statements which are undecidable but not provably undecidable

If the undecidability of a statement is a meta-mathematical theorem, then perhaps the existence of statements which are undecidable and non provably undecidable is a meta-meta-mathematical theorem. See the post:
 Are there statements that are undecidable but not provably undecidable
and its positive answer.

There are statements which are independent but not provably independent

If the independece of a statement is a meta-mathematical theorem, then the existence of statements which are independent and non provably independent is a meta-meta-mathematical theorem.
See the post:  Are there statements that are undecidable but not provably undecidable (undecidable is here synonymous of independent) and the positive answer under ZFC (assuming its consistence).