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.
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.
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.
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.
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.
Sieg W., Herband analyses Arch. Math. Logic 30 (1991), 409–441.
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.
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.
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(Conferenza tenuta l'11 maggio 1992)
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Sieg, W. Effectiveness and provability. Seminario Mat. e. Fis. di Milano 61, 219–230 (1991). https://doi.org/10.1007/BF02925207
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DOI: https://doi.org/10.1007/BF02925207