Skip to main content
Log in

Effectiveness and provability

  • Conferenze
  • Published:
Rendiconti del Seminario Matematico e Fisico di Milano Aims and scope Submit manuscript

Sunto

Tra le sfaccettature della ricerca logica contemporanea vi è la caratterizzazione delle funzioni dimostrabilmente totali in teorie deboli dell'analisi. Questo è il tema della nostra discussione. Utilizziamo come paradigma una teoria introdotta da H. Friedman evidenziandone le correlazioni con problematiche fondazionali ben più vaste.

Summary

The report details a facet of current logical work, namely characterizing the provably total functions of weak theories for analysis. That is described paradigmatically for a theory introduced by H. Friedman. However, the connection to broader foundational concerns is emphasized throughout.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Bibliography

  • Buss S.,Bounded Arithmetic; Bibliopolis, 1986.

  • Dedekind R. Stetigkeit und irrationale Zahlen; Braunschweig, 1872.

  • Dedekind R. Was sind und was sollen die Zahlen; Braunschweig, 1888.

  • Gödel K. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik 38 (1931), 173–198.

    Article  Google Scholar 

  • Gödel K., On undecidable propositions of formal mathematical systems; Lecture Notes, Princeton, 1934, reprinted in:The Undecidable (M. Davis, ed.), New York, 1965, 39–71.

  • Hilbert D., Über den Zahlbegriff: Jahresberichte der Deutschen Mathematiker-Vereinigung 8 (1900), 180–194.

    Google Scholar 

  • Howard W., Hereditarily majorizable functionals of finite type; in: Lecture Notes in Mathematics 344; Springer-Verlag, 1973, 454–461.

  • Kreisel G., On the interpretation of non-finitist proofs I; J. Symbolic Logic 16 (1951), 241–267.

    Article  MathSciNet  MATH  Google Scholar 

  • Kronecker L. Über den Zahlgebriff; published in 1887, reprinted inWerke, Vol. III, Part 1, Teubner, 1899, 251–274.

  • Luckhardt H., Herbrand-Analysen zweier Beweise des Satzes von Roth: polynomiale Anzahlschranken; J. Symbolic Logic, 54 (1989), 234–263.

    Article  MathSciNet  MATH  Google Scholar 

  • Sieg W., Herband analyses Arch. Math. Logic 30 (1991), 409–441.

    Article  MathSciNet  MATH  Google Scholar 

  • Sieg W., Mechanical procedures and mathematical experience; to appear in:Mathematics and Mind, A. George (ed.), Oxford University Press.

  • Simpson S. G., Unprovable theorems and fast-growing functions; Contemporary Mathematics vol. 65, 1987, 359–394.

    MathSciNet  Google Scholar 

  • Tait W. W., Normal derivability in classical logic; in:The syntax and semantics of infinitary languages, J. Barwise (ed.), Lecture Notes in Mathematics 72, 1968, 204–236.

Download references

Author information

Authors and Affiliations

Authors

Additional information

(Conferenza tenuta l'11 maggio 1992)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sieg, W. Effectiveness and provability. Seminario Mat. e. Fis. di Milano 61, 219–230 (1991). https://doi.org/10.1007/BF02925207

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02925207

Keywords

Navigation