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.
A note on the ordinal analysis of RCA0 + WO(σ) / Carlucci, Lorenzo; Mainardi, Leonardo; Rathjen, Michael. - 11558:(2019), pp. 144-155. (Intervento presentato al convegno Computability in Europe 2019 tenutosi a Durham; United Kingdom) [10.1007/978-3-030-22996-2_13].
A note on the ordinal analysis of RCA0 + WO(σ)
Carlucci, Lorenzo
;Mainardi, Leonardo;
2019
Abstract
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.| File | Dimensione | Formato | |
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