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Reflection using the derivability conditions

Matthews, Seán and Simpson, Alex K.

MPI-I-94-234. July 1994, 14 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
We extend arithmetic with a new predicate $Pr$, giving axioms for it
based on first order versions of L\"ob's derivability conditions. We
hoped that the addition of a reflection schema mentioning $Pr$ would
then give a non-conservative extension of the original arithmetic
theory. The paper investigates this possiblity. It is shown that,
under special conditions, the extension is indeed non-conservative.
However in general such extensions turn out to be conservative.
Categories / Keywords: Proof theory, reflection
References to related material:

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  AUTHOR = {Matthews, Se{\'a}n and Simpson, Alex K.},
  TITLE = {Reflection using the derivability conditions},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-94-234},
  MONTH = {July},
  YEAR = {1994},
  ISSN = {0946-011X},