Aberth, O.
1971
The failure in computable analysis of a classical existence theorem for differential equations,
Proc. Amer. Math. Soc.
30, 151–156
Aberth, O.
1980
Computable analysis,
McGraw-Hill:New York
Ahlfors, L. V.
1953
Complex Analysis,
McGraw-Hill: New York
Baez, J.C.
1983
Recursivity in quantum mechanics,
Trans. Amer. Math. Soc. 280, 339–350
Beeson, M.J.
1985
Foundations of constructive mathematics,
Springer: Heidelberg, New York
Bishop, E.A.
1967
Foundations of constructive analysis,
McGraw-Hill: New York
Bishop, E.A.
1970
Mathematics as a numerical language,
Intuitionism and Proof Th.; 1968 Buffalo
53–71; ed. by Kino, A., Myhill, J., Vesley, R.E.. North Holland: Amsterdam
Bjshop, E.A., Bridges, D.S.
1985
Constructive analysis,
Springer: Heidelberg, New York
Blum, L., Shub, M., Smale, S.
On a theory of computation and complexity over the real numbers: NP completeness, récursive functions and universal machines (to appear in Bull. Amer. Math. Soc.)
Bridges, D.S.
1979
Constructive functional analysis,
Pitman Publ.: Belmont, London v + 203pp
Brouwer, L.E.J.
1908
The unreliability of the logical principles (Dutch), Tijdsch. Wijsbegeerte
2, 152–158; transl. in: Coll. Works I, 107–111 (1975) (English)
Brouwer, L.E.J.
1975
Collected works I,
North Holland: Amsterdam
Brouwer, L.E.J.
1981
Brouwer's Cambridge lectures on intuitionism,
Cambridge Univ. Pr.: Cambridge, GB
Caldwell, J., Pour-El, B.M.
1975
On a simple definition of computable function of a real variable—with applications to functions of a complex variable,
Z. Math. Logik Grundlagen Math. 21, 1–19
Cleave, J.P.
1969
The primitive recursive analysis of ordinary differential equations and the complexity of their solutions,
J. Comp. Syst. Sci.
3, 447–455
Cook, S.A.
1971
The complexity of theorem proving procedures,
ACM Symp. Th. of Comput. (3); 1971 Shaker Heights
151–158
Cutland, N.J.
1980
Computability. An introduction to recursive function theory,
Cambridge Univ. Pr.: Cambridge, GB
Dalen van, D.
1973
Lectures on intuitionism,
Cambridge Summer School Math. Log.; 1971 Cambridge, GB 1–94; ed. by Rogers, H., Mathias, A.R.D.. Lect. Notes Math. 337, Springer: Heidelberg, New York
Davis, M.D.
1958
Computability and unsolvability,
McGraw-Hill: New York
Denef, J., Lipshitz, L.
1984
Power series solutions of algebraic differential equations,
Math. Ann. 267, 213–238
Dieudonné, J.A.
1969
Foundations of modern analysis,
Academic Pr.: New York
Dunford, N., Schwartz, J.T.
1958
Linear Operators, Part I,
Intersci. Publ.: New York
Feferman, S.
1977
Theories of finite type related to mathematical practice,
Handb. of Math. Logic
913–971; ed. by Barwise, J.. Stud. Logic Found. Math. 90, North Holland: Amsterdam
Feferman, S.
1979
Constructive theories of functions and classes,
Logic Colloq.; 1978 Mons
159–224; ed. By Boffa, M., Dalen van, D., McAloon, K.. Stud. Logic Found. Math. 97, North Holland: Amsterdam
Feferman, S.
1984
Between constructive and classical mathematics, Computation and Proof Theory, Logic Colloq.; 1983 Aachen
2, 143–162; ed. by Börger, E., Oberschelp, W., Richter, M.M., Schinzel, B., Thomas, W.. Lect. Notes Math. 1104, Springer: Heidelberg, New York
Friedman, H.M., Ker-I, Ko, 1982
Computational complexity of real functions,
Theor. Comput. Sci. 20, 323–352
Friedman, H.M.
1984
The computational complexity of maximization and integration,
Adv. Math.
53, 80–98
Goodstein, R.L.
1961
Recursive analysis,
North Holland: Amsterdam
Grzegorczyk, A.
1955
Computable functionals,
Fund. Math.
42, 168–202
Grzegorczyk, A.
1957
On the definitions of computable real continuous functions,
Fund. Math. 44, 61–71
Grzegorczyk, A.
1959
Some approaches to constructive analysis,
Constructivity in Math.; 1957 Amsterdam
43–61; ed. by Heyting, A.. Stud. Logic Found. Math., North Holland: Amsterdam
Halmos, P.R.
1950
Measure theory,
Van Nostrand: New York
Halmos, P.R.
1951
Introduction to Hilbert space,
Chelsea: New York
Hauck, J.
1981
Berechenbarkeit in topologischen Räumen mit rekursiver Basis,
Z. Math. Logik Grundlagen Math. 27, 473–480
Hauck, J.
1984
Zur Wellengleichung mit konstruktiven Randbedingungen,
Z. Math. Logik Grundlagen Math. 30, 561–566
Hellwig, G.
1964
Partial differential equations,
Blaisdell: New York
Heyting, A.
1956
Intuitionism. An introduction,
North Holland: Amsterdam
Huang, W., Nerode, A.
1985
Application of pure recursion theory in recursive analysis (Chinese), Shuxue Xuebao 28/5, 625–635
Hyland, J.M.E.
1982
Applications of constructivity,
Int. Congr. Log., Meth. and Phil, of Sci. (6, Proa); 1979 Hannover 145–152; ed. by Cohen, L.J., Łos, J., Pfeiffer, H., Podewski, K.-P.. Stud. Logic Found. Math. 104, North Holland: Amsterdam
Kalantari, L, Weitkamp, G.
1985
Effective topological spaces I: A definability theory. II: A hierarchy,
Ann. Pure Appl. Logic
29, 1–27,207–224
Karp, R.M.
1972
Reducibility among combinatorial problems,
Compl. of Computer Computation; 1972 York-town Heights
85–103; edited by Miller, R.E., Thatcher, J.W., Bohlinger, J.D.. Plenum Publ.: New York
Klaua, D.
1961
Konstruktive Analysis,
Dt. Verlag Wiss.: Berlin
Kleene, S.C.
1952
Introduction to metamathematics,
North Holland: Amsterdam
Kleene, S.C.
1956
A note on computable functions,
Indag. Math. 18, 275–280
Ker-I, Ko
1983
On the computational complexity of ordinary differential equations,
Inform, and Control
58, 157–194
Kreisel, G., Lacombe, D.
1957
Ensembles récursivement mesurables et ensembles récursivement ouverts ou fermés,
C. R. Acad. Sci., Paris
245,1106–1109
Kreisel, G.
1958
Review of “Meschkowski, H.: ‘Zur rekursiven Funktionentheorie’,
Acta Math.
95(1956), 9–23”, MR 19, 238
Kreisel, G.
1974
A notion of mechanistic theory,
Synthese 29, 11–16
Kreisel, G.
1982
Brouwer's Cambridge lectures on intuitionism,
Canad. Phil. Rev. 2, 249–251
Kreitz, C, Weihrauch, K.
1984
A unified approach to constructive and recursive analysis,
Computation and Proof Theory, Logic Colloq.; 1983 Aachen
2, 259–278; edited by Boerger, E., Oberschelp, W., Richter, M.M., Schinzel, B.
Thomas, W., Lect. Notes Math. 1104, Springer: Heidelberg, New York
Kushner, B.A.
1973
Lectures on constructive mathematical analysis (Russian), Nauka: Moskva 447pp; transl.: Amer. Math. Soc: Providence (1984) (English)
Lachlan, A.H.
1963
Recursive real numbers,
J. Symb. Logic
28, 1–16
Lacombe, D.
1955a
Extension de la notion de fonction récursive aux fonctions d'une ou plusieurs variables réelles. I,
C. R. Acad. Sci., Paris
240, 2478–2480
Lacombe, D.
1955b
Extension de la notion de fonction récursive aux fonctions d'une ou plusieurs variables reelles II, III,
C. R. Acad. Sci., Paris
241, 13–14,151–153
Lacombe, D.
1955c
Remarque sur les opérateurs récursifs et sur les fonctions récursives d'une variable réelle,
C. R. Acad. Sci., Paris
241, 1250–1252
Lacombe, D.
1957a
Quelques propriétés d'analyse récursive,
C. R. Acad. Sci., Paris
244, 838–840, 996–997
Lacombe, D.
1957b
Les ensembles récursivement ouverts ou fermés, et leurs applications à l'analyse récursive,
C. R. Acad. Sci., Paris
245, 1040–1043
Lacombe, D.
1958
Sur les possibilites d'extension de la notion de fonction récursive aux fonctions d'une ou plusieurs variables réelles,
Raisonn. en Math, et Sci. Expér.; 1955
Paris
67–71, Colloq. Int. CNRS. 70, CNRS Inst. B. Pascal: Paris 140pp
Lacombe, D.
1959
Quelques procédés de definition en topologie récursive,
Constructivity in Math.; 1957 Amsterdam
129–158 ed. by Heyting, A.. Stud. Logic Found. Math., North Holland: Amsterdam
Loomis, L.H.
1953
An introduction to abstract harmonic analysis,
Van Nostrand: New York
Mazur, S.
1963
Computable analysis,
PWN: Warsaw
Metakides, G., Nerode, A.
1982
The introduction of non-recursive methods into mathematics,
Brouwer Centenary Symp.; 1981 Noordwijkerhout
319–335; in Troelstra, A.S., Dalen van, D. (eds.) (1982)
Metakides, G., Nerode, A., Shore, R.A.
1985
Recursive limits on the Hahn-Banach theorem, E. Bishop—Reflection on Him & Research; 1983 San Diego
85–91; edited by Rosenblatt, M.. Contemp. Math. 39, Amer. Math. Soc: Providence
Moschovakis, Y.N.
1964
Recursive metric spaces,
Fund. Math. 55, 215–238
Moschovakis, Y.N.
1966
Notation systems and récursive ordered fields,
Compos. Math. 17, 40–71
Mostowski, A.
1957
On computable sequences,
Fund. Math. 44, 37–51
Mycielski, J.
1981
Analysis without actual infinity,
J. Symb. Logic
46, 625–633
Myhill, J.R.
1953
Criteria of constructibility for real numbers,
J. Symb. Logic
18, 7–10
Myhill, J.R.
1971
A recursive function, defined on a compact interval and having a continuous derivative that is not recursive,
Michigan Math. J.
18, 97–98
Orevkov, V.P.
1963
A constructive mapping of the square onto itself displacing every constructive point (Russian), Dokl. Akad. Nauk SSSR
152, 55–58; transl. in: Sov. Math., Dokl. 4, 1253–1256 (1963) (English)
Petrovskij, I.G.
1967
Partial differential equations,
Saunders: Philadelphia
Pour-El, M.B.
1974
Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers), Trans. Amer. Math. Soc. 199, 1–28
Pour-El, M.B., Richards, I.
1979
A computable ordinary differential equation which possesses no computable solution,
Ann. Math. Logic
17, 61–90
Pour-El, M.B., Richards, I.
1981
The wave equation with computable initial data such that its unique solution is not computable,
Adv. Math. 39, 215–239
Pour-El, M.B., Richards, I.
1983a
Computability and noncomputability in classical analysis,
Trans. Amer. Math. Soc.
275, 539–560
Pour-El, M.B., Richards, I.
1983b
Noncomputability in analysis and physics: a complete determination of the class of non-computable linear operators,
Adv. Math. 48, 44–74
Pour-El, M.B., Richards, I.
1984
Lp-computability in récursive analysis,
Proc. Amer. Math. Soc.
92, 93–97
Pour-El, M.B., Richards, I.
1987
The eigenvalues of an effectively determined self-adjoint operator are computable, but the sequence of eigenvalues is not, Adv. Math. 63, 1–41
Computability on a Banach space—the eigenvector theorem, (to appear)
Remmel, J.B.
1978
Recursively enumerable boolean algebras,
Ann. Math. Logic
15, 75–107
Rice, H.G.
1954
Recursive real numbers,
Proc. Amer. Math. Soc. 5, 784–791
Richardson, D.B.
1968
Some undecidable problems involving elementary functions of a real variable,
J. Symb. Logic
33, 514–520
Riesz, F., Sz.-Nagy, B.
1955
Functional analysis,
Ungar: New York and London
Robinson, R.M.
1951
Review of “Peter, R.: ‘Rekursive Funktionen’,Akad. Kiado, Budapest, 1951”, J. Symb. Logic
16, 280
RogersJr., H.
1967
Theory of recursive functions and effective computability,
McGraw-Hill: New York
Rosenbloom, P.C.
1945
An elementary constructive proof of the fundamental theorem of algebra,
Amer. Math. Mon. 52, 562–570
Rudin, W.
1973
Real and complex analysis,
McGraw-Hill: New York
Ščedrov, A.
1984
Differential equations in constructive analysis and in the récursive realizability topos,
J. Pure Appl. Algebra
33, 69–80
Schütte, K.
1977
Proof theory,
Springer: Heidelberg, New York
Shanin, N.A.
1962
Constructive real numbers and constructive function spaces (Russian), Tr. Mat. Inst. Steklov
67, 15–294; Akad. Nauk SSSR: Moskva; transl.: Amer. Math. Soc: Providence (1968) (English)
Shepherdson, J.C.
1976
On the definition of computable function of a real variable,
Z. Math. Logik Grundlagen Math. 22, 391–402
Shohat, J.A., Tamarkin, J.D.
1943
The problem of moments,
Amer. Math. Soc: Providence
Simpson, S.G.
1984
Which set existence axioms are needed to prove the Cauchy/Peano theorem for ordinary differential equations?,
J. Symb. Logic
49, 783–802
Soare, R.I.
1969
Recursion theory and Dedekind cuts,
Trans. Amer. Math. Soc. 140, 271–294
Soare, R.I.
1987
Recursively enumerable sets and degrees,
Springer: Heidelberg, New York
Specker, E.
1949
Nicht konstruktiv beweisbare Sätze der Analysis,
J. Symb. Logic
14, 145–158
Specker, E.
1959
Der Satz vom Maximum in der rekursiven Analysis,
Constructivity in Math.; 1957 Amsterdam
254–265; edited by Heyting, A. Stud. Logic Found. Math., North Holland: Amsterdam
Specker, E.
1969
The fundamental theorem of algebra in recursive analysis,
Constr. Aspects Fund. Thm. Algeb.; 1967 Zürich
321–329; edited by Dejon, B., Henrici, P.. Wiley and Sons: New York
Traub, J.F., Wasilkowski, G.W., Wozniakowski, H.
1988
Information-based complexity,
Academic Press Inc., Boston, New York
Troelstra, A.S.
1969
Principles of intuitionism,
Springer: Heidelberg, New York
Troelstra, A.S., Dalen van, D. (eds.) 1982
The L.E.J. Brouwer centenary symposium,
Stud. Logic Found. Math. 110, North Holland: Amsterdam
Tsejtin, G.S.
1959
Algorithmic operators in constructive complete separable metric spaces (Russian), Dokl. Akad. Nauk SSSR
128, 49–52
Tsejtin, G.S.
1962
Mean value theorems in constructive analysis (Russian), Tr. Mat. Inst. Steklov
67, 362–384; Akad. Nauk SSSR: Moskva; transl. in: Amer. Math. Soc, Transl., Ser. 2 98, 11–40 (1971) (English)
Tsejtin, G.S., Zaslavskij, I.D.
1962
On singular coverings and properties of constructive functions connected with them (Russian), Tr. Mat. Inst. Steklov
67, 458–502; Akad. Nauk SSSR: Moskva; transl. in: Amer. Math. Soc, Transl., Ser. 2 98, 41–89 (1971) (English)
Turing, A.M.
1936
On computable numbers, with an application to the “Entscheidungsproblem”,
Proc London Math. Soc, Ser. 2
42, 230–265; corr. ibid. 43, 544–546 (1937)
Weyl, H.
1918
Das Kontinuum,
Veit: Leipzig
Wolfram, S.
1985
Undecidability and intractability in theoretical physics,
Phys. Rev. Lett. 54, 735–738
Zaslavskij, I.D.
1955
Disproof of some theorems of classical analysis in constructive analysis (Russian), Usp. Mat. Nauk 10/4, 209–210
Zaslavskij, I.D.
1962
Some properties of constructive real numbers and constructive functions (Russian), Tr. Mat. Inst. Steklov
67, 385–457 Akad. Nauk SSSR: Moskva; transl. in: Amer. Math. Soc, Transl., Ser. 2 57, 1–84 (1966) (English)
Zygmund, A.
1959
Trigonometric series. Vol. I, II,
Cambridge Univ. Pr.: Cambridge, GB
