 Feferman–Schütte ordinal

The Feferman–Schütte ordinal is a specific ordinal number that arises in the context of proof theory and the study of formal systems, particularly in relation to the proof strength of various formal systems in arithmetic. It is denoted by \( \Gamma_0 \) and is associated with certain subsystems of second-order arithmetic. The ordinal itself is significant because it characterizes the proof-theoretic strength of specific formal systems, notably those that can express certain principles of mathematical induction.