Choice principles in hyperuniverses

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


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



    Upload a copy of this work     Papers currently archived: 92,931

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Pigeonhole and Choice Principles.Wolfgang Degen - 2000 - Mathematical Logic Quarterly 46 (3):313-334.
Choice principles and constructive logics.David Dedivi - 2004 - Philosophia Mathematica 12 (3):222-243.
Choice principles from special subsets of the real line.E. Tachtsis & K. Keremedis - 2003 - Mathematical Logic Quarterly 49 (5):444.
Comparison of the axioms of local and global universality.Marco Forti & Furio Honsell - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (13‐16):193-196.
Choice sequences and informal rigour.A. S. Troelstra - 1985 - Synthese 62 (2):217 - 227.
Rigit Unary Functions and the Axiom of Choice.Wolfgang Degen - 2001 - Mathematical Logic Quarterly 47 (2):197-204.
Choice Principles and Compactness Conditions.Bernhard Banaschewski - 1998 - Mathematical Logic Quarterly 44 (3):427-430.
Addiction: An Emergent Consequence of Elementary Choice Principles.Gene M. Heyman - 2013 - Inquiry: An Interdisciplinary Journal of Philosophy 56 (5):428 - 445.


Added to PP

15 (#972,895)

6 months
3 (#1,042,169)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

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.

View all 6 references / Add more references