On Arithmetical First-Order Theories Allowing Encoding and Decoding of Lists

@article{Cgielski1999OnAF,
  title={On Arithmetical First-Order Theories Allowing Encoding and Decoding of Lists},
  author={Patrick C{\'e}gielski and Denis Richard},
  journal={Theor. Comput. Sci.},
  year={1999},
  volume={222},
  pages={55-75}
}
In Computer Science, n-tuples and lists are usual tools ; we investigate both notions in the framework of first-order logic within the set of nonnegative integers. Gödel had firstly shown that the objects which can be defined by primitive recursion schema, also can be defined at first-order, using natural order and some coding devices for lists. Secondly he had proved that this encoding can be defined from addition and multiplication. We show this can be also done with addition and a weaker… CONTINUE READING
Highly Cited
This paper has 37 citations. REVIEW CITATIONS

References

Publications referenced by this paper.
Showing 1-10 of 11 references

The theory of integer multiplication with order restricted to primes is decidable,The

Maurin Françoise
Journal of Symbolic Logic, • 1997

Equivalence of some questions in mathematical logic with some conjectures in number theory, Number theory and applications, (Mollin ed.)

Richard Denis
NATO Asi Series, Series C : Mathematical and Physical Sciences, • 1988

Über formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik

Gödel Kurt
English translation in Van Heijenoort, 1967 and in Collected Works, • 1986

Grundlagen der Mathematik 2, Springer, 2nd ed

Hilbert David, Bernays Paul
Fondements des mathématiques 2, Prépublication LLAIC1, • 1970

Grundlagen der Mathematik 1, Springer, 2nd ed

Hilbert David, Bernays Paul
Fondements des mathématiques 1, Prépublication LLAIC1, • 1968

Recursive programming

W. Dijkstra Edsger
Numerische Mathematik, • 1960

Uber eine Eigenschaft des Inbegroffes aller reellen zlgebraischen Zahlen

Cantor Georg
Journ. für die reine und angew. Math., • 1930