dc.creator | Fernández Margarit, Alejandro | es |
dc.creator | Lara Martín, Francisco Félix | es |
dc.date.accessioned | 2019-06-24T08:20:15Z | |
dc.date.available | 2019-06-24T08:20:15Z | |
dc.date.issued | 2004 | |
dc.identifier.citation | Fernández Margarit, A. y Lara Martín, F.F. (2004). Induction, minimization and collection for Δ n+1 (T)–formulas. Archive for Mathematical Logic, 43 (4), 505-541. | |
dc.identifier.issn | 0933-5846 | es |
dc.identifier.uri | https://hdl.handle.net/11441/87546 | |
dc.description.abstract | For a theory T, we study relationships among IΔ n +1 (T), LΔ n+1 (T) and B * Δ n+1 (T). These theories are obtained restricting the schemes of induction, minimization and (a version of) collection to Δ n+1 (T) formulas. We obtain conditions on T (T is an extension of B * Δ n+1 (T) or Δ n+1 (T) is closed (in T) under bounded quantification) under which IΔ n+1 (T) and LΔ n+1 (T) are equivalent. These conditions depend on Th Πn +2 (T), the Π n+2 –consequences of T. The first condition is connected with descriptions of Th Πn +2 (T) as IΣ n plus a class of nondecreasing total Π n –functions, and the second one is related with the equivalence between Δ n+1 (T)–formulas and bounded formulas (of a language extending the language of Arithmetic). This last property is closely tied to a general version of a well known theorem of R. Parikh. Using what we call Π n –envelopes we give uniform descriptions of the previous classes of nondecreasing total Π n –functions. Π n –envelopes are a generalization of envelopes (see [10]) and are closely related to indicators (see [12]). Finally, we study the hierarchy of theories IΔ n+1 (IΣ m ), m≥n, and prove a hierarchy theorem. | es |
dc.description.sponsorship | Ministerio de Educación y Cultura DGES PB96-1345 | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Springer | es |
dc.relation.ispartof | Archive for Mathematical Logic, 43 (4), 505-541. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.title | Induction, minimization and collection for Δ n+1 (T)–formulas | 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 | DGES PB96-1345 | es |
dc.relation.publisherversion | https://link.springer.com/article/10.1007/s00153-003-0197-8 | es |
dc.identifier.doi | 10.1007/s00153-003-0197-8 | es |
idus.format.extent | 34 | es |
dc.journaltitle | Archive for Mathematical Logic | es |
dc.publication.volumen | 43 | es |
dc.publication.issue | 4 | es |
dc.publication.initialPage | 505 | es |
dc.publication.endPage | 541 | es |