Semantical completeness theorems in logic and algebra
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- by Vladimir Lifschitz
- Proc. Amer. Math. Soc. 79 (1980), 89-96
- DOI: https://doi.org/10.1090/S0002-9939-1980-0560591-4
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Abstract:
A few well-known algebraic theorems, including the Nullstellensatz and a form of the duality theorem of Farkas-Minkowsky, are shown to be corollaries to the completeness of the hyper-resolution method in proof theory.References
- J. A. Robinson, Automatic deduction with hyper-resolution, Internat. J. Comput. Math. 1 (1965), 227–234. MR 188081, DOI 10.1007/978-3-642-81952-0_{2}7
- Ju. V. Matijasevič, A metamathematical approach to proving theorems in discrete mathematics, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 49 (1975), 31–50, 177 (Russian, with English summary). Theoretical applications of the methods of mathematical logic, I. MR 0376327
- Bruno Scarpellini, On the metamathematics of rings and integral domains, Trans. Amer. Math. Soc. 138 (1969), 71–96. MR 239941, DOI 10.1090/S0002-9947-1969-0239941-4 W. Whiteley, Logic and invariant theory, Ph.D. Thesis, M.I.T., Cambridge, Mass., 1971. S. C. Kleene, Permutability of inferences in Gentzen’s Calculi LK and LJ, Mem. Amer. Math. Society, no. 10, 1952.
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 89-96
- MSC: Primary 03F65; Secondary 03B99
- DOI: https://doi.org/10.1090/S0002-9939-1980-0560591-4
- MathSciNet review: 560591