PA− | 𝐏𝐀⁻ | Finitely axiomatized fragment of PA | |
Iopen | 𝐈open | PA− + Induction of open formula | |
IΣ0 | 𝐈𝚺₀ | PA− + Induction of Σ0 formula | Theory IΣ0 |
IΣ0+Ω1 | 𝐈𝚺₀ + Ω₁ | IΣ0 + Ω1-axiom | |
EA | 𝐄𝐀 | Elementary arithmetic | |
IΣ1 | 𝐈𝚺₁ | PA− + Induction of Σ1 formula | Theory IΣ1 |
PA | 𝐏𝐀 | Peano arithmetic | |