Friedman/Simpson programme: for each mathematical theorem φ, identify the minimal set-existence axioms over RCA₀ required to prove φ. The 'big five' (RCA₀, WKL₀, ACA₀, ATR₀, Π¹₁-CA₀) classify most of classical mathematics.
Friedman/Simpson programme: for each mathematical theorem φ, identify the minimal set-existence axioms over RCA₀ required to prove φ. The 'big five' (RCA₀, WKL₀, ACA₀, ATR₀, Π¹₁-CA₀) classify most of classical mathematics.