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Largest fixed points of set continuous operators and Boffa's Anti‐Foundation
Author(s) -
Muraki Hisato
Publication year - 2005
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.200410039
Subject(s) - mathematics , axiom , fixed point , axiom of choice , schema (genetic algorithms) , fixed point theorem , discrete mathematics , zermelo–fraenkel set theory , urelement , mathematical economics , set (abstract data type) , pure mathematics , set theory , mathematical analysis , computer science , geometry , machine learning , programming language
In Aczel [1], the existence of largest (written “greatest” in Barwise and Moss [2]) fixed points of set continuous operators is proved assuming the schema version of dependent choices in Zermelo‐Fraenkel set theory without the axiom of Foundation. In the present paper, we study whether the existence of largest fixed points of set continuous operators is provable without the schema version of dependent choices, using Boffa's weak antifoundation axioms. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)