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Herbrand strategies and the ”greater deducibility” relation. (English) Zbl 0449.03006

MSC:

03B10 Classical first-order logic
03F99 Proof theory and constructive mathematics

Citations:

Zbl 0358.02030
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Full Text: DOI

References:

[1] G. E. Mints, ?Herbrand’s theorem,? in: Mathematical Theory of Logical Deduction [in Russian], Moscow (1967), pp. 311?350.
[2] S. Yu. Maslov, ?The inverse method and tactics for determining deducibility for a calculus with functional signs,? Tr. Mat. Inst. Akad. Nauk SSSR,121, 14?56 (1972).
[3] G. S. Tseitin, ?Deduction complexity in enumeration of statements,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,8, 234?259 (1968).
[4] S. Yu. Maslov, ?The relationship between tactics of the inverse method and of the resolution method,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,16, 136?146 (1969).
[5] G. S. Tseitin and A. A. Chubaryan, ?Some bounds for the length of logical deductions in classical calculus of statements,? Tr. VTs Arm. SSR and Erevansk. Univ.,8, 57?64 (1975).
[6] S. Yu. Maslov, ?On the search for a deduction in calculi of a general type,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,32, 59?65 (1972).
[7] A. O. Slisenko, ?A property of recursively enumerable sets which contain ?complicatedly deducible? formulas,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,20, 200?207 (1971). · Zbl 0222.02045
[8] A. O. Slisenko, ?A finite approach to the optimization of algorithms for establishing deducibility,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,49, 123?130 (1975).
[9] S. Yu. Maslov and S. A. Norgela, ?The analysis of recursively enumerable sets and the search for a deduction,? Third Pan-Soviet Conference on Mathematical Logic (Abstracts), Novosibirsk (1974), pp. 138?140.
[10] E. L. Post, ?Formal reductions of the general combinatorial decision problem,? Am. J. Math.,65, No. 2, 197?215 (1943). · Zbl 0063.06327 · doi:10.2307/2371809
[11] S. Yu. Maslov, ?The concept of strict representability in the general theory of calculi,? Tr. Mat. Inst. Akad. Nauk SSSR,93, 3?42 (1967).
[12] B. A. Kushner, Lectures in Constructive Mathematical Analysis [in Russian], Moscow (1973). · Zbl 0547.03040
[13] M. L. Minsky, ?Recursive unsolvability of Post’s problem of ?Tag? and other topics in theory of Turing machines,? Ann. Math.,74, No. 3, 437?455 (1961). · Zbl 0105.00802 · doi:10.2307/1970290
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