@inproceedings{0b4a5b60d61a40e89d1cbab123a7a2c0,

title = "Reflection using the derivability conditions",

abstract = "The authors consider a recursively axiomatized arithmetic T with a new primitive predicate Pr characterized by axioms (C1)–(C3) based on L{\"o}b{\textquoteright}s derivability conditions (denote this new theory by T ' ). It is shown that T ' +R, where R is the reflection scheme, is conservative over T. It is also proved that the theory IΣ 1 ' +R contains Peano arithmetic PA where IΣ 1 ' is arithmetic with induction for Σ 1 formulas in the language with Pr and axioms (C1)–(C3) as well as that PA ' +R is a conservative extension of PA.",

author = "Sean Matthews and Alex Simpson",

year = "1996",

month = may,

day = "30",

language = "English",

isbn = "9780824796068",

series = "Lecture Notes Pure Applied Mathematics",

publisher = "MARCEL DEKKER",

pages = "603 -- 616",

editor = "Aldo Ursini and Agliano, {Paolo }",

booktitle = "Proceedings of the international conference dedicated to the memory of Roberto Magari, April 26–30, 1994, Pontignano, Italy.",

}