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This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed. Later, we turn to least universes, strictness and name induction. Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent(More)
This investigation has employed the "innocent bystander" type of experimental design to determine whether soluble cytotoxic factor(s) are released during interactions between human peripheral blood lymphocytes (PBL) and NK-sensitive target cells. PBL cocultured with NK-sensitive Molt-4 or K562 target cells in the lower well of a miniaturized Marbrook(More)
In applicative theories the recursion theorem provides a term rec which solves recursive equations. However, it is not provable that a solution obtained by rec is minimal. In the present paper we introduce an applicative theory in which it is possible to define a least fixed point operator. Still, our theory has a standard recursion theoretic interpretation(More)
Due to strictness problems, usually the syntactical definition of Frege structures is conceived as a truth theory for total applicative theories. To investigate Frege structures in a partial framework we can follow two ways. First, simply by ignoring undefinedness in the truth definition. Second, by introducing of a certain notion of pointer. Both(More)
In diesem Aufsatz wird erstmals die Hilbertsche Antinomie vollständig publiziert. David Hilbert hat sie während seiner Auseinandersetzun-gen mit der Cantorschen Mengenlehre gefunden. Seinen Angaben zu-folge wurde Ernst Zermelo durch sie zu seiner Version der Zermelo-Russellschen Antinomie angeregt. Es handelt sich um die Antinomie der Menge aller durch(More)