Subsystems of quine’s “new foundations” with predicativity restrictions

Notre Dame Journal of Formal Logic

Volumn 40, Issue 2, 1999, Pages 183-196

  Randall Holme, M ^a  

^a BOISE STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85015121134     PISSN: 00294527     EISSN: 19390726     Source Type: Journal    
DOI: 10.1305/ndjfl/1038949535     Document Type: Article

References (11)

1. Crabbé, M., “On the consistency of an impredicative subsystem of Quine’s NF,” The Journal of Symbolic Logic, vol. 47 (1982), pp. 131-36.
2. Crabbé, M., “Ramification et prédicativité,” Logique et Analyse, vol. 84 (1978), pp. 399-419.
3. Hailperin, T., “A set of axioms for logic,” The Journal of Symbolic Logic, vol. 9 (1944), pp. 1-19.
4. Holmes, M. R., “The equivalence of NF-style set theories with ‘tangled’ type theories; the construction of omega-models of predicative NF (and more),” The Journal of Symbolic Logic, vol. 60 (1995), pp. 178-89.
5. Holmes, M. R., Elementary Set Theory with a Universal Set, Academia, Louvain-laNeuve, 1998.
6. Jensen, R. B., “On the consistency of a slight(?) modification of Quine’s NF,” Synthese, vol. 19 (1969), pp. 250-63.
7. Quine, W. V., “New foundations for mathematical logic,” American Mathematical Monthly, vol. 44 (1937), pp. 70-80.
8. Quine, W. V., “On ordered pairs,” The Journal of Symbolic Logic, vol. 10 (1945), pp. 95-96.
9. Rogers, H., The Theory of Recursive Functions and Effective Computability, The MIT Press, Cambridge, 1988. See Theorem XIII, Corollary XIIIa, Corollary XIV, in Section 16.2, pp. 386-90.
10. Specker, E. P., “The axiom of choice in Quine’s ‘New foundations for mathematical logic’,” Proceedings of the National Academy of Sciences of the USA, vol. 39 (1953), pp. 972-75.
11. Specker, E. P., “Typical ambiguity,” pp. 116-124 in Logic, Methodology and Philosophy of Science, edited by E. Nagel, Stanford University Press, Palo Alto, 1962.