dc.creator | Cordón Franco, Andrés | es |
dc.creator | Fernández Duque, David | es |
dc.creator | Joosten, Joost J. | es |
dc.creator | Lara Martín, Francisco Félix | es |
dc.date.accessioned | 2019-06-27T10:30:19Z | |
dc.date.available | 2019-06-27T10:30:19Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Cordón Franco, A., Fernández Duque, D., Joosten, J.J. y Lara Martín, F.F. (2017). Predicativity through Transfinite Reflection. The Journal of Symbolic Logic, 82 (3), 787-808. | |
dc.identifier.issn | 0022-4812 | es |
dc.identifier.uri | https://hdl.handle.net/11441/87646 | |
dc.description.abstract | Let T be a second-order arithmetical theory, Λ a well-order, λ < Λ and X ⊆ ℕ. We use as a formalization of “φ is provable from T and an oracle for the set X, using ω-rules of nesting depth at most λ”.
For a set of formulas Γ, define predicative oracle reflection for T over Γ (Pred–O–RFNΓ(T)) to be the schema that asserts that, if X ⊆ ℕ, Λ is a well-order and φ ∈ Γ, then
In particular, define predicative oracle consistency (Pred–O–Cons(T)) as Pred–O–RFN{0=1}(T).
Our main result is as follows. Let ATR0 be the second-order theory of Arithmetical Transfinite Recursion, be Weakened Recursive Comprehension and ACA be Arithmetical Comprehension with Full Induction. Then,
We may even replace by the weaker ECA0, the second-order analogue of Elementary Arithmetic.
Thus we characterize ATR0, a theory often considered to embody Predicative Reductionism, in terms of strong reflection and consistency principles. | es |
dc.description.sponsorship | Ministerio de Educación, Cultura y Deporte MTM2014-59178-P | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | The Association for Symbolic Logic | es |
dc.relation.ispartof | The Journal of Symbolic Logic, 82 (3), 787-808. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.title | Predicativity through Transfinite Reflection | 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 | MTM2014-59178-P | es |
dc.relation.publisherversion | https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/predicativity-through-transfinite-reflection/B9CB0810C3B89C01BB9FA51B4EB4943C | es |
dc.identifier.doi | 10.1017/jsl.2017.30 | es |
idus.format.extent | 22 | es |
dc.journaltitle | The Journal of Symbolic Logic | es |
dc.publication.volumen | 82 | es |
dc.publication.issue | 3 | es |
dc.publication.initialPage | 787 | es |
dc.publication.endPage | 808 | es |