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In this note we study some local properties ofω-stable groups of finite Morley rank.
In spite of the fact that the Z.F. universe is not well-ordered, it behaves in some respects like the ordinals. It is possible to define on it the usual operations of addition, multiplication and exponentiation, which enjoy similar properties to those on the ordinals. Further when restricted to...
The busy beaver problem of Rado  is reexamined for the case of Turing machines given by quadruples rather than quintuples. Moreover several printing symbols are allowed. Some values of the corresponding beaver function are given and it is shown that this function for a fixed number of states...
In this paper we give a new and comparatively simple proof of the following theorem by Girard :
We consider expansions of models of Peano arithmetic to models ofA
−AC which consist of families of sets definable by nonstandard formulas.
This paper gives a recursive generalization of a strong notation system of ordinals, which was devellopped by Jäger . The generalized systemT(V′) is based on a hierarchy of Veblen-functions for inaccessible ordinals. The definition ofT(V′) assumes the existence of a weak Mahlo-ordinal. The...
A recursive notation system of a strong segment of ordinals was developped by Jäger . An unessential modified versionT(J) of this notation system was described in . In the following, the well-ordering ofT(J) is proved in a formal system of second order arithmetic with the axiom schema ofΠ...
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