TRANSFINITE RECURSION IN HIGHER REVERSE MATHEMATICS.
In this paper we investigate the reverse mathematics of higher-order analogues of the theory $$ATR_0$$ within the framework of higher order reverse mathematics developed by Kohlenbach [11]. We define a theory $$RCA_0^3$$, a close higher-type analogue of the classical base theory $$RCA_0$$ which is e...
| Publicado en: | Journal of Symbolic Logic Vol. 80; no. 3; pp. 940 - 970 |
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| Formato: | Artículo |
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Cambridge University Press
Sep2015
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=108608234&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 108608234 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Sep2015 vid: 80 iid: 3 pid: 15979 pub: Cambridge University Press artinfo: ui: 108608234 10.1017/jsl.2015.2 ppf: 940 ppct: 30 formats: tig: atl: TRANSFINITE RECURSION IN HIGHER REVERSE MATHEMATICS. aug: au: SCHWEBER, NOAH affil: DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA, BERKELEY BERKELEY, CALIFORNIA 94720, USA E-mail: schweber@math.berkeley.edu su: Transfinite numbers Cardinal numbers Reverse mathematics First-order phase transitions Reversible computing sug: subj: Transfinite numbers Cardinal numbers Reverse mathematics First-order phase transitions Reversible computing keyword: determinacy forcing higher reverse mathematics reverse mathematics set theory ab: In this paper we investigate the reverse mathematics of higher-order analogues of the theory $$ATR_0$$ within the framework of higher order reverse mathematics developed by Kohlenbach [11]. We define a theory $$RCA_0^3$$, a close higher-type analogue of the classical base theory $$RCA_0$$ which is essentially a conservative subtheory of Kohlenbach’s base theory $$RCA_{\rm{0}}^\omega$$. Working over $$RCA_0^3$$, we study higher-type analogues of statements classically equivalent to $$ATR_0$$, including open and clopen determinacy, and examine the extent to which $$ATR_0$$ remains robust at higher types. Our main result is the separation of open and clopen determinacy for reals, using a variant of Steel’s tagged tree forcing; in the presentation of this result, we develop a new, more flexible framework for Steel-type forcing. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2015 holdings: @attributes: islocal: N |
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