Takeuti–Feferman–Buchholz ordinal

The Takeuti–Feferman–Buchholz ordinal, often denoted by \( \Omega \), is a significant ordinal in the realm of proof theory and mathematical logic. It arises in the study of ordinal analysis of the system \( \text{PRA} \) (Primitive Recursive Arithmetic) and is particularly associated with the strength of formal systems and their consistency proofs.