Artículo
Predicativity through Transfinite Reflection
Autor/es | Cordón Franco, Andrés
Fernández Duque, David Joosten, Joost J. Lara Martín, Francisco Félix |
Departamento | Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial |
Fecha de publicación | 2017 |
Fecha de depósito | 2019-06-27 |
Publicado en |
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Resumen | 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 ... 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. |
Identificador del proyecto | MTM2014-59178-P |
Cita | 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. |
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