Abstract
We formulate epsilon substitution method for elementary analysisEA (second order arithmetic with comprehension for arithmetical formulas with predicate parameters). Two proofs of its termination are presented. One uses embedding into ramified system of level one and cutelimination for this system. The second proof uses non-effective continuity argument.
Similar content being viewed by others
References
Ackermann, W.: Begründung des Tertium non datur mittels der Hilbertschen Theorie der Widerspruchsfreiheit. Math. Ann.93, 1–36 (1925)
Ackermann, W.: Zur Widerspruchsfreiheit der Zahlentheorie. Math. Ann.117, 162–164 (1940)
Bourbaki, N.: Theorie des ensembles. Paris: Hermann 1958
Gentzen, G.: Die Widerspruchsfreiheit der reinen Zahlentheorie. Math. Ann. 112, 493–565 (1936)
Girard, J.-Y.: Une extension de l'interpretation de Gödel a l'analyse et la application a l'elimination des coupures dans l'analyse et la theorie des types. Proc. 2nd Scand. Logic Symp., pp. 63–92, Amsterdam: North-Holland 1972
Hilbert, D.: Probleme der Grundlegung der Mathematik. Math. Ann.102, 1–9 (1929)
Hilbert, D., Bernays, P.: Grundlagen der Mathematik, Bd.2. Berlin Heidelberg New York: Springer 1970
Kreisel, G.: On the interpretation of non-finitist proofs I. J. Symb. Logic16, 241–267 (1951)
Kreisel, G.: On the Interpretation of Non-finitist proofs II. J. Symb. Logic17, 43–58 (1952)
Mints, G.: Simplified consistency proof for arithmetic (Russian). Proc. Estonian Acad. Sci. Fiz.-Math.31, 376–382 (1982)
Mints, G.: Epsilon substitution method for the theory of hereditarily finite sets (Russian). Proc. Eston. Acad. Sci. Fiz.-Math.N2, 154–164 (1989)
Mints, G.: Gentzen-type systems and Hilbert's epsilon substitution method, Vol. I. In: Logic, Method and Philosophy of Science, Vol. IX, pp. 91–122. Amsterdam: Elsevier (1994)
Mints, G., Tupailo, S.: Epsilon substitution method for elementary analysis. Report No. CSLI-93-175, 1993, CSLI, Stanford University (1993)
Kleene, S.C.: Introduction to Metamathematics. New York Toronto: Van Nostrand 1952
von Neumann, J.: Zur Hilbertschen Beweistheorie. Math. Z.26, 1–46 (1927)
Schutte, K.: Proof Theory. Berlin Heidelberg New York: Springer 1977
Tait, W.: Functionals defined by transfinite recursion. J. Symb. Logic30, 155–174 (1965)
Tait, W.: The substitution method. J. Symb. Logic30, 175–192 (1965)
Weyl, H.: David Hilbert and his mathematical work. Bull. Amer. Math. Soc.50, 612–654 (1944)