First-Order Frege Theory is Undecidable
Tóm tắt
The system whose only predicate is identity, whose only nonlogical vocabulary is the abstraction operator, and whose axioms are all first-order instances of Frege's Axiom V is shown to be undecidable.
Tài liệu tham khảo
Burgess, J. (1998): On a consistent subsystem of Frege's ‘Grundgesetze’, Notre Dame J. Formal Logic 39, 274–278.
Heck, R. (1996): The consistency of predicative fragments of Frege's Grundgesetze der Arithmetik, History and Philosophy of Logic 17, 209–220.
Parsons, T. (1987): On the consistency of the first-order portion of Frege's logical system, Notre Dame J. Formal Logic 28, 161–188; reprinted in W. Demopoulos (ed.), Frege's Philosophy of Mathematics, Harvard Univ. Press, 1995, pp. 422–431.