2001 seminar talk: Some words on well-foundedness principles over definable sets
Talk held by Arnold Beckmann (TU Wien, Uni Münster) at the KGRC seminar on 2001-12-13.
Well-foundedness principles are used in the definition of proof theoretic ordinals. If the 2nd order quantification in this definition is restricted to definable sets (e.g. arithmetical sets in case of Peano Arithmetic) we obtain "pathological" proof theoretic ordinals by a result of Kreisel. Does the situation differ for other pairs of theories and definable sets? Or, is there a way out of this misery?