Choice principles in hyperuniverses

Annals of Pure and Applied Logic 77 (1):35-52 (1996)
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Abstract

It is well known that the validity of Choice Principles is problematic in non-standard Set Theories which do not abide by the Limitation of Size Principle. In this paper we discuss the consistency of various Choice Principles with respect to the Generalized Positive Comprehension Principle . The Principle GPC allows to take as sets those classes which can be specified by Generalized Positive Formulae, e.g. the universe. In particular we give a complete characterization of which choice principles hold in Hyperuniverses. Hyperuniverses are structures which arose independently in Non-well-founded Set Theory and in Mathematical Semantics of Concurrent Programming Languages and are hitherto the only existing models of GPC. Hyperuniverses are naturally endowed with a κ-compact uniform κ-topology and are uniformly isomorphic to their exponential space, i.e. the space of their closed subsets endowed with the Exponential Uniformity

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Marco Forti
University of Pisa

References found in this work

New Foundations for Mathematical Logic.W. V. Quine - 1937 - Journal of Symbolic Logic 2 (2):86-87.
Non-Well-Founded Sets.Peter Aczel - 1988 - Palo Alto, CA, USA: Csli Lecture Notes.
The consistency problem for positive comprehension principles.M. Forti & R. Hinnion - 1989 - Journal of Symbolic Logic 54 (4):1401-1418.

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