Haskell B. Curry - Foundations of Mathematical Logic

This bibliography is intended to list only items cited in the text. Citations are made by authors name and abbreviated title in brackets. These abbreviated titles are listed here alphabetically under each author, except that abbreviations beginning with rev, which refer to reviews, are listed after the other works by the same author.

In the case of joint authors, the group of authors is considered as a new author. When it is not desirable to mention all the authors, the abbreviation et al . is used; this means that the work referred to is by the author mentioned and one or more others. Cross references to the additional authors will be made through the index.

A citation without an authors name (expressed or implied) is to a work by Curry, or in the case of [CLg], Curry and Feys. In the case of cross references in this bibliography, however, the reference is to another work by the same author, unless otherwise indicated.

Ordinarily the initials of the given names of the authors are not given in making citations. They may be found from this bibliography. In the cases where the initials do not suffice for identification, the given names are stated.

When a work contains two or more volumes, or otherwise detached parts, reference to a particular volume or part is made by putting the volume or part number inside the brackets after a period. Different editions of the same work are distinguished by numerical subscripts. Thus, under Whitehead and Russell, [PMt.I2] is the second edition of the first volume of [PMt]. Occasionally this device is used to distinguish works which have the same title, even though they are scarcely different editions of the same work.

References to parts of a work are made either by page numbers or the natural divisions of the work cited. Such references are frequently included in the brackets.

Journals are abbreviated according to the practice of Mathematical Reviews (see vol. 19, pp. 14171430, and similar lists in earlier volumes). When Mathematical Reviews does not list a journal, an abbreviation is used that conforms to their practice in principle.

In referring to parts of journals, the volume number is written first, then a colon, then the page numbers, then (in parentheses) the presumed date of publication. Everyone knows that the actual date of publication is sometimes difficult to determine. In such cases the best information available has been used, but an exhaustive inquiry has not been made.

In transliterating Russian, the system described in Math. Rev., :1433, and ascribed to Science Abstracts, has been followed. This requires fewer special letters than other systems.

Ackermann, W.

[BSI]

Begrndung einer strengen Implikation, J. Symb. Logic, :113128 (1956).

[SCD]

Solvable Cases of the Decision Problem, Amsterdam, 1954.

Ajdukiewicz, K.

[TCD]

Three Concepts of Definition, Logique et analyse, n.s., 1e Anne: 115126 (1958).

American Mathematical Society

[SLM]

Structure of Language and its Mathematical Aspects, Proc. 12t h Symposium in Applied Mathematics, New York, 1960 (published 1961).

Anderson, A. R.

[CTS]

Completeness Theorems for the Systems E of Entailment and EQ of Entailment with Quantification, Tech. Rep . 6, Contract SAR/Nonr609 (16) (Problem Solving and Social Interaction) for U.S. Office of Naval Research, New Haven, Conn., 1959.

Anderson, A. R., and N. D. Belnap, Jr.

[PCE]

The Pure Calculus of Entailment, ditto manuscript prepared at Yale University, May 5, 1960. See also Anderson [CTS].

Asser, G.

[AFP]

ber die Ausdrucksfhigkeit des Prdikatenkalkls der ersten Stufe mit Funktionalen, Z. Math. Logik Grundlagen Math., :250264 (1956).

[NPA]

Normierte Postsche Algorithmen, Z. Math. Logik Grundlagen Math., :323333 (1959).

[TLA]

Theorie der logischen Auswahlfunktionen, Z. Math. Logik Grundlagen Math., :3068 (1957).

[TMM]

Turing-Maschinen und Markowsche Algorithmen, Z. Math. Logik Grundlagen Math., :346365 (1959).

Bachmann, H.

[TZh]

Transfinite Zahlen, Berlin, 1955.

Becker, O.

[ELg]

Einfhrung in die Logistik, Meisenheim am Glan, 1951.

Behmann, H.

[PKL]

Der Prdikatenkalkl mit limitierten Variablen. Grundlegung einer natrlichen exakten Logik, J. Symb. Logic. :112140 (1959).

[WLM]

Zu den Widersprchen der Logik und der Mengenlehre, Jber. Deutsch. Math. Verein, :3748 (1931).

Bennett, A. A.

[SSO]

Semi-serial Order, Amer. Math. Monthly, :418423 (1930).

Bergmann, G.

[FHN]

Freges Hidden Nominalism, Philos. Rev., :437459 (1958).

Bernays, P.

[AUA]

Axiomatische Untersuchung des Aussagenkalkuls der Principia mathematica, Math. Z ., :305320 (1926).

[BSB]

Zur Beurteilung der Situation in der beweistheoretischen Forschung, Theoria (Madrid), :153154 (1952).

[HGG]

ber Hilberts Gedanken zur Grundlegung der Arithmetik, Jber. Deutsch Math. Verein., :1019 (1922).

[LC1]

Logical Calculus, notes by Bernays with assistance of F. A. Ficken at Institute for Advanced Study, Princeton, N.J., 19351936.

[PMt]

Sur le platonisme dans les mathmatiques, Enseignement Math., :5269 (19351936).

[QMA]

Sur les questions mthodologiques actuelles de la thorie hilbertienne de la demonstration, Les Entretiens de Zurich sur les fondements et la mthode des sciences mathmatiques (December 69, 1938), 1941, pp. 144152, Discussion, pp. 153161.

[rev. C]

Review of Curry [DNF] and [SLD], J . Symb. Logic , :266268 (1953).

Bernays, P., and A. Fraenkel

[AST]

Axiomatic Set Theory, Amsterdam, 1958.

Berstein, B. A.

[FBA]

On Finite Boolean Algebras, Amer. J. Math., :733742 (1935).

Berry, G. D. W.

[OSL]

Symposium: On the Ontological Significance of the Lwenheim-Skolem Theorem, Academic Freedom, Logic, and Religion (American Philosophical Association, Eastern Division), Philadelphia, 1953, pp. 3955. See also Myhill [OSL].

Beth, E. W.

[CSL]

Construction smantique de la logique intuitionniste, Le raisonnement en mathmatiques et en sciences exprimentales (Colloques internationaux du Centre National de la Recherche Scientifique), vol. 70, 1958, pp. 7784.

[CTL]

Some Consequences of the Theorem of Lwenheim-Skolem-Gdel-Malcev, Nederl. Akad. Wetensch. Proc., ser. A, 56(= Indag. Math., 15):6671 (1953).

[FMt]

The Foundations of Mathematics, Amsterdam, 1959.

[SCI]

Semantic Construction of Intuitionistic Logic, Meded. Kon. Nederl. Akad. Wetensch., Letterkunde, n.s., :357388 (1956).

[SEF]

Semantic Entailment and Formal Derivability, Meded. Kon. Nederl. Akad. Wetensch. Letterkunde, n.s., :309342 (1955).

[SLG]

Symbolische Logik und Grundlegung der exakten Wissenschaften, Bibliographische Einfhrungen in das Studium der Philosophie, 1948.

[TPT]

A Topological Proof of the Theorem of Lwenheim-Skolem-Gdel, Nederl. Akad. Wetensch., ser. A., 54(= Indag. Math ., 13):436444 (1951).

[VIn]

Verstand en Intuitie, Algemeen Nederl. Tijdschr. Wijsbegeerte en Psychologie, :213224 (19531954).

Birkhoff, Garrett

[CSA]

On the Combination of Subalgebras, Proc. Cambridge Philos. Soc., :441 464 (1933).

[LTh]

Lattice Theory, American Mathematical Society, 1sted., 1940; 2ded., 1948.

Birkhoff, G., and J. von Neumann

[LQM]

The Logic of Quantum Mechanics, Ann. of Math., (2) :823842 (1936).

Black, M.

[NMt]

The Nature of Mathematics: A Critical Survey, New York, 1934.