2019-06-272019-06-272004Cordón Franco, A., Fernández Margarit, A. y Lara Martín, F.F. (2004). On the quantifier complexity of Δ n+1 (T)– induction. Archive for Mathematical Logic, 43 (3), 371-398.0933-5846https://hdl.handle.net/11441/87645In this paper we continue the study of the theories IΔ n+1 (T), initiated in [7]. We focus on the quantifier complexity of these fragments and theirs (non)finite axiomatization. A characterization is obtained for the class of theories such that IΔ n+1 (T) is Π n+2 –axiomatizable. In particular, IΔ n+1 (IΔ n+1 ) gives an axiomatization of Th Π n+2 (IΔ n+1 ) and is not finitely axiomatizable. This fact relates the fragment IΔ n+1 (IΔ n+1 ) to induction rule for Δ n+1 –formulas. Our arguments, involving a construction due to R. Kaye (see [9]), provide proofs of Parsons’ conservativeness theorem (see [16]) and (a weak version) of a result of L.D. Beklemishev on unnested applications of induction rules for Π n+2 and Δ n+1 formulas (see [2]).application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/InductionΔ n+1FormulasQuantifier complexityinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1007/s00153-003-0198-7