Ricerc@Sapienza

We fill an apparent gap in the literature by giving a short and self-contained proof that the ordinal of the theory RCA0+WO(σ) is σ^ω , for any ordinal σ satisfying ω⋅σ=σ (e.g., ω^ω , ω^ω^ω , ε0 ). Theories of the form RCA0+WO(σ) are of interest in Proof Theory and Reverse Mathematics because of their connections to a number of well-investigated combinatorial principles related to various subsystems of arithmetic.