An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz

Studia Logica

Volumn 58, Issue 1, 1997, Pages 79-97

  Cignoli, Roberto ^a   Mundici, Daniele ^b  

^a Facultad Ciencias Exactas/Naturales   (Argentina)

^b UNIVERSITY OF MILAN   (Italy)

Author keywords

Completeness of the ukasiewicz calculus; Infinite valued logic; MV algebra

Indexed keywords

EID: 0002924587     PISSN: 00393215     EISSN: 15728730     Source Type: Journal    
DOI: 10.1023/A:1004991931741     Document Type: Article

References (10)

1. CHANG, C. C., 1958, 'Algebraic analysis of many-valued logics, Trans. Amer. Math. Soc. 88, 467-490.
2. CHANG, C. C., 1959, 'A new proof of the completeness of the Łukasiewicz axioms', Trans. Amer. Math. Soc. 93, 74-80.
3. CIGNOLI, R., 1993, 'Free lattice-ordered abelian groups and varieties of MV-algebras', In: "Proceedings of the IXth Latin American Symposium on Mathematical Logic, I", Notas de Lógica Matemática, Universidad National del Sur, Bahía Bianca, Argentina 38, 113-118.
4. MANGANI, P., 1973, 'On certain algebras related to many-valued logics', (Italian), Bollettino Unione Matematica Italiana 8, 68-78.
5. MUNDICI, D., 1986, 'Interpretation of AF C-algebras in Łukasiewicz sentential calculus', J. Functional Analysis 65, 15-63.
6. MUNDICI, D., 1993, 'Ulam game, Łukasiewicz logic, and AF C -algebras', Fundamenta Informaticae 18, 151-161.
7. PANTI, G., 1995, 'A geometric proof of the completeness of the calculus of Łukasiewicz', J. Symbolic Logic, 60, 563-578.
8. ROSE, A., and J. B. ROSSER, 1958, 'Fragments of many-valued statement calculi', Trans. Amer. Math. Soc. 87, 1-53.
9. TARSKI, A., J. ŁUKASIEWICZ, 1956, 'Investigations into the Sentential Calculus', In: "Logic, Semantics, Metamathematics", Oxford University Press, 38-59, reprinted by Hackett Publishing Company, Indianapolis, 1983.
10. ULAM, S. M., 1976, Adventures of a Mathematician, Scribner's, New York.