Bounds extracted by Kreisel from ineffective proofs. (English) Zbl 0896.03005

Luckhardt, Horst

Odifreddi, Piergiorgio (ed.), Kreiseliana: about and around Georg Kreisel. Wellesley, MA: A K Peters. 289-300 (1996).

Focusing on Georg Kreisel’s contributions, the author intends to show how mathematical logic and in particular proof theory can be used to make substantial contributions to mathematics. His examples are Littlewood’s theorem of 1914, Hilbert’s Nullstellensatz (1893), Hilbert’s 17th problem (1900), \(L\)-series, and the mathematical analysis of the proofs of Roth’s theorem (1955).
For the entire collection see [Zbl 0894.03002].

Reviewer: V.Peckhaus (Erlangen)

MSC:

03-03	History of mathematical logic and foundations
03F35	Second- and higher-order arithmetic and fragments
01A60	History of mathematics in the 20th century
11U09	Model theory (number-theoretic aspects)
12L12	Model theory of fields

Keywords:

proof theory; bounds extracted from ineffective proofs