Well- and non-well-founded Fregean extensions

Conference item

George Boolos has described an interpretation of a fragment of ZFC in a consistent second-order theory whose only axiom is a modification of Frege's inconsistent Axiom V. We build on Boolos's interpretation and study the models of a variety of such theories obtained by amending Axiom V in the spirit of a limitation of size principle. After providing a complete structural description of all well-founded models, we turn to the non-well-founded ones. We show how to build models in which foundati...

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Authors: Jane, I; Uzquiano, G

• Publication status: Published
• Host title: JOURNAL OF PHILOSOPHICAL LOGIC
• Volume: 33
• Issue: 5
• Pages: 437-465
• Publication date: 2004-10-01
• DOI: 10.1023/B:LOGI.0000046129.22633.96
• EISSN: 1573-0433
• ISSN: 0022-3611
• Keywords: second-order set theory; extensions; New V; George Boolos; Axiom V; non-well-founded sets; Gottlob Frege; AFA; ZFC