dc.creator | Cordón Franco, Andrés | es |
dc.creator | Fernández Margarit, Alejandro | es |
dc.creator | Lara Martín, Francisco Félix | es |
dc.date.accessioned | 2019-06-21T08:50:37Z | |
dc.date.available | 2019-06-21T08:50:37Z | |
dc.date.issued | 2006 | |
dc.identifier.citation | Cordón Franco, A., Fernández Margarit, A. y Lara Martín, F.F. (2006). Envelopes, indicators and conservativeness. Mathematical Logic Quaterly, 52 (1), 51-70. | |
dc.identifier.issn | 0942-5616 | es |
dc.identifier.uri | https://hdl.handle.net/11441/87542 | |
dc.description.abstract | A well known theorem proved (independently) by J. Paris and H. Friedman states that BΣn +1 (the fragment of Arithmetic given by the collection scheme restricted to Σn +1‐formulas) is a Πn +2‐conservative extension of IΣn (the fragment given by the induction scheme restricted to Σn ‐formulas). In this paper, as a continuation of our previous work on collection schemes for Δn +1(T )‐formulas (see [4]), we study a general version of this theorem and characterize theories T such that T + BΣn +1 is a Πn +2‐conservative extension of T . We prove that this conservativeness property is equivalent to a model‐theoretic property relating Πn ‐envelopes and Πn ‐indicators for T . The analysis of Σn +1‐collection we develop here is also applied to Σn +1‐induction using Parsons' conservativeness theorem instead of Friedman‐Paris' theorem.
As a corollary, our work provides new model‐theoretic proofs of two theorems of R. Kaye, J. Paris and C. Dimitracopoulos (see [8]): BΣn +1 and IΣn +1 are Σn +3‐conservative extensions of their parameter free versions, BΣ–n +1 and IΣ–n +1. | es |
dc.description.sponsorship | Junta de Andalucía TIC-137 | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Wiley | es |
dc.relation.ispartof | Mathematical Logic Quaterly, 52 (1), 51-70. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Collection principles | es |
dc.subject | Initial segments | es |
dc.subject | Indicators | es |
dc.subject | Envelopes | es |
dc.subject | Conservation results | es |
dc.title | Envelopes, indicators and conservativeness | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial | es |
dc.relation.projectID | TIC-137 | es |
dc.relation.publisherversion | https://onlinelibrary.wiley.com/doi/abs/10.1002/malq.200410055 | es |
dc.identifier.doi | 10.1002/malq.200410055 | es |
idus.format.extent | 20 p. | es |
dc.journaltitle | Mathematical Logic Quaterly | es |
dc.publication.volumen | 52 | es |
dc.publication.issue | 1 | es |
dc.publication.initialPage | 51 | es |
dc.publication.endPage | 70 | es |
dc.identifier.sisius | 6634558 | es |