caa a22 4500 388039949 CHVBK 20180307125018.0 cr unu---uuuuu 161130e199809 xx s 000 0 eng 10.2307/2586713 doi S0022481200014602 pii (NATIONALLICENCE)cambridge-10.2307/2586713 Σ2 Induction and infinite injury priority argument, Part I: Maximal sets and the jump operator [Elektronische Daten] The study of recursion theory on models of fragments of Peano arithmetic has hitherto been concentrated on recursively enumerable (r.e.) sets and their degrees (with a few exceptions, such as that in [2] on minimal degrees). The reason for such a concerted effort is clear: priority arguments have occupied a central position in post Friedberg-Muchnik recursion theory, and after almost forty years of intensive development in the subject, they are still the essential tools on which investigations of r.e. sets and their degrees depend. There are two possible approaches to the study within fragments of arithmetic: To give a general analysis of strategies, and identify their proof-theoretic strengths (for example in [6] on infinite injury priority methods), or to consider specific theorems in recursion theory, and, if possible, pinpoint the exact levels of induction provably equivalent to the theorems. The work reported in this paper belongs to the second approach. More precisely, we single out two infinitary injury type constructions of r.e. sets—one concerning maximal sets and the other based on the notion of the jump operator—to be the topics of study. Copyright © Association for Symbolic Logic 1998 Chong C. T. Department of Mathematics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore 119260, E-mail: chongct@math.nus.edu.sg Yang Yue Department of Mathematics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore 119260, E-mail: matyangy@nus.edu.sg The Journal of Symbolic Logic Cambridge University Press 63/3(1998-09), 797-814 0022-4812 63:3<797 1998 63 JSL https://doi.org/10.2307/2586713 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586713 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chong C. T. Department of Mathematics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore 119260, E-mail: chongct@math.nus.edu.sg NATIONALLICENCE 700 1- Yang Yue Department of Mathematics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore 119260, E-mail: matyangy@nus.edu.sg NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/3(1998-09), 797-814 0022-4812 63:3<797 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge