La théorie des fonctions récursives et ses applications. (Exposé d'information générale)
Lacombe, D.
Bulletin de la Société Mathématique de France, Tome 88 (1960), p. 393-468 / Harvested from Numdam
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@article{BSMF_1960__88__393_0,
     author = {Lacombe, Daniel},
     title = {La th\'eorie des fonctions r\'ecursives et ses applications. (Expos\'e d'information g\'en\'erale)},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     volume = {88},
     year = {1960},
     pages = {393-468},
     doi = {10.24033/bsmf.1555},
     mrnumber = {23 \#A60},
     zbl = {0156.25201},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/BSMF_1960__88__393_0}
}

Lacombe, D. La théorie des fonctions récursives et ses applications. (Exposé d'information générale). Bulletin de la Société Mathématique de France, Tome 88 (1960) pp. 393-468. doi : 10.24033/bsmf.1555. http://gdmltest.u-ga.fr/item/BSMF_1960__88__393_0/

[1] Ackermann (Wilhelm). - Solvable cases of the decision problem. - Amsterdam, North-Holland publishing Company, 1954 (Studies in Logic and the Foundations of Mathematics). | Zbl 0056.24505

[2] Addison (John W.). - Separation principles in the hierarchies of classical and effective descriptive set theory, Fund. Math., t. 46, 1958, p. 123-135. | MR 24 #A1209 | Zbl 0091.05201

[3] Brown (Edgar H.). - Finite computability of Postnikov complexes, Annals of Math., Series 2, t. 65, 1957, p. 1-20. | MR 18,753a | Zbl 0077.16804

[4] Church (Alonzo). - On the concept of a random sequence, Bull. Amer. math. Soc., t. 46, 1940, p. 130-135. | JFM 66.0601.01 | MR 1,149a | Zbl 0022.36904

[5] Davis (Martin). - Computability and unsolvability. - New-York, Mc Graw-Hill Book Company, 1958 (Mc Graw-Hill Series in Information Processing and Computers). | Zbl 0080.00902

[6] Friedberg (Richard M.). - Two recursively enumerable sets of incomparable degrees of unsolvability (solution of Post's problem, 1944), Proc. Nat. Acad. Sc. U.S.A., t. 43, 1957, p. 236-238. | Zbl 0080.24302

[7] Friedberg (Richard M.). - 4-quantifier completeness : a Banach-Mazur functional not uniformly partial recursive, Bull. Acad. polon. Sc., t. 6, 1958, p. 1-5. | MR 20 #3071 | Zbl 0084.24902

[8] Gilmore (C.). - A proof method for quantification theory : its justification and realization, I. M. B. J. of Research and Development, t. 4, 1960, p. 28-35. | MR 23 #B3113 | Zbl 0097.00301

[9] Grzegorczyk (Andrzej). - Some approaches to constructive analysis, Constructivity in mathematics, Proc. Coll. Amsterdam, 1957, p. 43-61. - Amsterdam, North-Holland publishing Company, 1959 (Studies in Logic and the Foundations of Mathematics). | Zbl 0088.01701

[10] Kleene (S. C.). - Finite axiomatizability of theories in the predicate calculus using additional predicate symbols, Memoirs Am. math. Soc., n° 10, 1952, p. 27-68. | MR 14,439d | Zbl 0047.25001

[11] Kleene (S. C.). - Introduction to metamathematics. - Amsterdam, North-Holland publishing Company; Groningen, Noordhoff, 1952 (Bibliotheca Mathematica, 1). | MR 14,525m | Zbl 0047.00703

[12] Kleene (S. C.). - Hierarchies of number-theoretic predicates, Bull. Amer. math. Soc., t. 61, 1955, p. 193-213. | MR 17,4f | Zbl 0066.25901

[13] Kleene (S. C.). - Recursive functionals and quantifiers of finite type I, Trans. Amer. math. Soc., t. 91, 1959, p. 1-52. | MR 21 #1273 | Zbl 0088.01301

[14] Kleene (S. C.). - Countable functionals, Constructivity in mathematics, Proc. Coll. Amsterdam 1957 ; p. 81-100. - Amsterdam, North-Holland publishing Company, 1959 (Studies in Logic and the Foundations of Mathematics). | Zbl 0100.24901

[15] Kleene (S. C.). - Mathematical Logic : constructive and non-constructive operations, Proc. Intern. Congr. Math. [1958. Edinburgh] ; p. 137-153. - Cambridge, at the University Press, 1960. | Zbl 0126.01903

[16] Kreisel (Georg). - Mathematical significance of consistency proofs, J. of symb. Logic, t. 23, 1958, p. 155-182. | MR 22 #6710 | Zbl 0088.01502

[17] Kreisel (Georg). - Interpretation of analysis by means of constructive functionals of finite type, Constructivity in mathematics, Proc. Coll. Amsterdam, 1957 ; p. 101-128. - Amsterdam, North-Holland publishing Company, 1959. (Studies in Logic and the Foundations of Mathematics). | Zbl 0134.01001

[18] Kreisel (Georg). - La prédicativité, Bull. Soc. math. France, t. 88, 1960, p. 371-391. | Numdam | MR 23 #A800 | Zbl 0131.00604

[19] Kreisel (Georg). - Set theoric problems suggested by the notion of potentiel totality, Proceedings of the Symposium on infinitistic methods in the foundations of mathematics [1959. Warszawa] ; p. 103-140. - Warszawa, 1960. | Zbl 0199.01401

[20] Kreisel (G.) et Lacombe (D.). - Ensembles récursivement mesurables et ensembles récursivement ouverts ou fermés, C. R. Acad. Sc. Paris, t. 245, 1957, p. 1106-1109. | MR 22 #3680 | Zbl 0079.00901

[21] Kreisel (G.), Lacombe (D.) and Shoenfield (J. R.). - Partial recursive functionals and effective operations, Constructivity in mathematics, Proc. Coll. Amsterdam 1957 ; p. 290-297. - Amsterdam, North-Holland publishing Company, 1959 (Studies in Logic and the Foundations of Mathematics). | Zbl 0178.32201

[22] Lacombe (Daniel). - Quelques propriétés d'analyse récursive, C. R. Acad. Sc. Paris, 244, 1957, p. 996-997. | Zbl 0077.01601

[23] Lacombe (Daniel). - Les ensembles récursivement ouverts ou fermés et leurs applications à l'analyse récursive, C. R. Acad. Sc. Paris, t. 245, 1957, p. 1040-1043. | Zbl 0078.00703

[24] Lacombe (Daniel). - Quelques procédés de définition en topologie récursive, Constructivity in mathematics, Proc. Coll. Amsterdam 1957 ; p. 129-158. Amsterdam, North-Holland publishing Company, 1959 (Studies in Logic and the Foundations of Mathematics). | Zbl 0089.00701

[25] Markov (A. A.). - The problem of homeomorphy [en russe], Proc. Intern. Congr. Math. [1958. Edinburgh] ; p. 300-306. - Cambridge, at the University Press, 1960. | Zbl 0119.25201

[26] Myhill (J.) and Dekker (J. C. E.). - Recursive equivalence types. - Berkeley, University of California (à paraître). | Zbl 0249.02021

[27] Myhill (J.) and Shepherdson (J. C.). - Effective operations on partial recursive functions, Z. für math. Logik und Grundl. der Math., t. 1, 1955, p. 310-317. | MR 17,1039b | Zbl 0068.24706

[28] Novikov (P. S.). - Sur l'insolubilité algorithmique du problème des mots [en russe], Trudy Mat. Inst. Steklov, t. 44, 1955, p. 143. | MR 17,706b | Zbl 0068.01301

[29] Porte (Jean). - Une simplification de la théorie de Turing, Actes du 1er Congrès international de Cybernétique [1956. Namur] ; p. 251-280. - Paris, Gauthier-Villars ; Namur, Association internationale de Cybernétique, 1958.

[30] Porte (Jean), - Systèmes de Post et algorithmes de Markov, Cybernetica, n° 2 (1958), 1959.

[31] Putnam (Hilary). - An unsolvable problem in number theory, J. of symb. Logic (à paraître).

[32] Quine (W. V.). - Concatenation as a basis for arithmetic, J. of symb. Logic, t. 11, 1946, p. 105-114. | MR 8,307b | Zbl 0063.06362

[33] Rabin (Michael O.). - Recursive unsolvability of group theoric problems, Annals of Math., Series 2, t. 67, 1958, p. 172-194. | Zbl 0079.24802

[34] Rabin (Michael O.). - On recursively enumerable and arithmetic models of set theory, J. of symb. Logic, t. 23, 1958, p. 408-416. | MR 22 #10908 | Zbl 0095.24601

[35] Rabin (Michael O.) and Scott (Dana). - Finite automata and their decision problems, I.B.M.J. of Research and Development, t. 3, 1959, p. 114-125. | MR 21 #2559 | Zbl 0158.25404

[36] Rogers (Hartley, Jr). - Gödel numberings of partial recursive functions, J. of symb. Logic, t. 23, 1958, p. 331-341. | Zbl 0088.01602

[37] Shepherdson (J. C.). - Representability of recursively enumerable sets in formal theories, Archiv für math. Logik und Grundlagenforschung (à paraître). | Zbl 0113.24305

[38] Spector (Clifford). - On degrees of recursive unsolvability, Annals of Math., Series 2, t. 64, 1956, p. 581-592. | MR 18,552d | Zbl 0074.01302

[39] Tarski (A.), Mostowski (A.) and Robinson (R. M.). - Undecidable theories. Amsterdam, North-Holland publishing Company, 1953 (Studies in Logic and the Foundations of Mathematics). | Zbl 0053.00401

[40] Tennenbaum (S.). - Non-archimedean models for arithmetic, Notices Amer. math. Soc., t. 6, 1959, p. 270.