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Theories of Arithmetics

NotationDescription
𝗣𝗔⁻Finitely axiomatized fragment of
𝗜𝗢𝗽𝗲𝗻 + Induction of open formula
𝗜𝚺₀ + Induction of formulaTheory
𝗜𝚺₀ + Ω₁ + -axiom
𝐄𝐀Elementary arithmetic
𝗜𝚺₁ + Induction of formulaTheory
𝗣𝗔Peano arithmetic