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COMPARISON OF THE AXIOMS OF LOCAL AND GLOBAL UNIVERSALITY
Author(s) -
Forti Marco,
Honsell Furio
Publication year - 1984
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19840301302
Subject(s) - universality (dynamical systems) , humanities , mathematics , axiom , philosophy , physics , geometry , quantum mechanics
1. In 1965 D. SCOTT introduced in an unpublished paper (see [S]) an axiom strongly contradicting the Axiom of Foundation. After him several authors, e.g. BOFFA ([I], [2]), HAJEK ([S]), considered the possibility of consistently replacing Foundation by axioms which postulate a strong non-well-foundedness of the membership relation. The authors examined this problem ([3], [ S ] ) , through a different approach, i.e. giving a “Free Construction Principle” for sets, while researching at the seminar on Foundations of Mathematics held by Prof. E. DE GIORGI a t the Scuola Normale Superiore in Pisa. The axioms derivable from this principle are studied in detail in [4].