The art of ordinal analysis
- Autores: Michael Rathjen
- Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé
, Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 45-70 - Idioma: inglés
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Resumen
Ordinal analysis of theories is a core area of proof theory whose origins can be traced back to Hilbert�s programme � the aim of whichwas to lay to rest allworries about the foundations of mathematics once and for all by securing mathematics via an absolute proof of consistency.
Ordinal-theoretic proof theory came into existence in 1936, springing forth from Gentzen�s head in the course of his consistency proof of arithmetic. The central theme of ordinal analysis is the classification of theories by means of transfinite ordinals that measure their �consistency strength� and �computational power�. The so-called proof-theoretic ordinal of a theory also serves to characterize its provably recursive functions and can yield both conservation and combinatorial independence results.
This paper intends to survey the development of �ordinally informative� proof theory from the work of Gentzen up to more recent advances in determining the proof-theoretic ordinals of strong subsystems of second order arithmetic.
