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Closed categories and the theory of proofs. (English) Zbl 0449.03054

MSC:
03F99 Proof theory and constructive mathematics
18A15 Foundations, relations to logic and deductive systems
18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
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[1] G. Kelly and S. MacLane, ?Coherence in closed categories,? J. Pure Appl. Algebra,1, No. 1, 97?140 (1971). · Zbl 0212.35001 · doi:10.1016/0022-4049(71)90013-2
[2] S. Eilenberg and G. Kelly, ?Closed categories,? Proc. Conf. on Categorical Algebra La Jolla, 1965, Springer-Verlag (1966), 421?562.
[3] G. E. Minc, Proof Theory and Category Theory [in Russian]. · Zbl 0514.03042
[4] G. E. Minc, ?Normalization of proofs,? Appendix to book by S. C. Kleene, Mathematical Logic [in Russian], Moscow (1973).
[5] D. Prawitz, Natural Deduction, a Proof Theoretical Study, Stockholm (1965). · Zbl 0173.00205
[6] G. E. Minc, Proof Theory (Arithmetic and Analysis). Algebra, Topology, Geometry [in Russian], Vol. 13, VINITI, Moscow (1975), pp. 5?49.
[7] J. Lambek, ?Deductive systems and categories. I,? Math. Systems Theory,2, No. 4, 287?318 (1968). · Zbl 0176.28901 · doi:10.1007/BF01703261
[8] J. Lambek, ?Deductive systems and categories. II,? Lect. Notes Math.,86, 76?122 (1969). · Zbl 0198.33701 · doi:10.1007/BFb0079385
[9] J. Lambek, ?Deductive systems and categories. III,? Lect. Notes Math.,274, 57?82 (1972). · Zbl 0244.18006 · doi:10.1007/BFb0073965
[10] D. Prawitz, ?Ideas and Results in Proof Theory,? Proc. 2 Scand. Logic Sympos., Amsterdam (1971), pp. 235?307.
[11] G. Kreisel, ?A survey of proof theory. II,? Proc. 2 Scand. Logic Sympos., Amsterdam (1971), pp. 109?170.
[12] K. Sch?tte, Beweistheorie, Berlin (1960).
[13] S. MacLane, ?Topology and logic as a source of algebra,? Bull. Am. Math. Soc.,82, No. 1, 1?40 (1976). · Zbl 0324.55001 · doi:10.1090/S0002-9904-1976-13928-6
[14] J. Zucker, ?The correspondence between cut-elimination and normalization,? Ann. Math. Log.,7, No. 1, 1?112 (1974). · Zbl 0298.02023 · doi:10.1016/0003-4843(74)90010-2
[15] M. Szabo, ?A categorical equivalence of proofs,? Notre Dame J. Form. Log.,15, No. 2, 171?191 (1974). · Zbl 0275.02033 · doi:10.1305/ndjfl/1093891297
[16] M. Szabo, Addendum (to [15]), Notre Dame J. Form. Log.
[17] C. Mann, ?The connection between equivalence of proofs and cartesian closed categories,? Proc. London Math. Soc.,31, No. 3, 289?310 (1975). · Zbl 0317.02036 · doi:10.1112/plms/s3-31.3.289
[18] P. Martin-L?f, ?Infinite terms and a system of natural deduction,? Compos. Math.,24, No. 1, 93?103 (1972). · Zbl 0237.02006
[19] G. Kelly, ?An abstract approach to coherence,? Lect. Notes Math.,281, 106?147 (1972). · Zbl 0243.18016 · doi:10.1007/BFb0059557
[20] S. Eilenberg and G. Kelly, ?A generalization of the functorial calculus,? J. Algebra,3, No. 3, 366?375 (1966). · Zbl 0146.02501 · doi:10.1016/0021-8693(66)90006-8
[21] A. Troelstra, ?Metamathematical investigation of intuitionistic arithmetic and analysis,? Lect. Notes Math.,344 (1974).
[22] G. E. Minc, ?A theorem on cut-elimination for relevant logic,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,32, 90?97 (1972).
[23] G. E. Minc, ?The independence of postulates of natural calculuses,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,8, 192?195 (1968). · Zbl 0174.00903
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