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• [1] Leon Henkin, A generalization of the concept of 𝜔-completeness, J. Symb. Logic 22 (1957), 1–14. MR 0095120 (20 #1626)
• [2] Leon Henkin, Completeness in the theory of types, J. Symbolic Logic 15 (1950), 81–91. MR 0036188 (12,70b)
• [1] A. Malcev Untersuchungen aus dem Gebiete der mathematischen Logik, Recueil Mathématique N.S. vol. 1 (1936) pp. 323-336.
• [1] John von Neumann Zur Einführung der transfiniten Zahlen, Acta litterarum ac scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, Sectio scientiarum mathematicarum vol. 1 (1923) pp. 199-208.
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• [1] John G. Kemeny Type theory vs. set theory, a Thesis at Princeton University (1949). (Abstract appeared on p. 78 of J. Symbolic Logic vol. 15 (1950)).
• [1] W. V. Quine Mathematical logic, New York, 1940; second printing, Cambridge, Mass., 1947.
• [2] W. V. Quine, Element and number, J. Symbolic Logic 6 (1941), 135–149. MR 0006326 (3,289a)
• [1] J. Barkley Rosser and Hao Wang, Non-standard models for formal logics, J. Symbolic Logic 15 (1950), 113–129. MR 0038307 (12,384c)
• [1] Arnold Schmidt, Über deduktive Theorien mit mehreren Sorten von Grunddingen, Math. Ann. 115 (1938), no. 1, 485–506 (German). MR 1513200, http://dx.doi.org/10.1007/BF01448954
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• [1] Alfred Tarski Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philosophica vol. 1 (1936) pp. 261-405. (Original in Polish, 1933.)
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• [1] Hao Wang, A new theory of element and number, J. Symbolic Logic 13 (1948), 129–137. MR 0026978 (10,229g)
• [2] Hao Wang, On Zermelo’s and von Neumann’s axioms for set theory, Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 150–155. MR 0029850 (10,670b)
• [3] Hao Wang, Remarks on the comparison of axiom systems, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 448–453. MR 0039661 (12,578j)
• [4] Hao Wang, Arithmetic translations of axiom systems, Trans. Amer. Math. Soc. 71 (1951), 283–293. MR 0043046 (13,198p), http://dx.doi.org/10.1090/S0002-9947-1951-0043046-1

Bibliography

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Paul Bernays A system of axiomatic theory, J. Symbolic Logic, Part I, vol. 2 (1937) pp. 65-77; Part II, vol. 6 (1941) pp. 1-17. MR 0003382 (2:210c)

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Kurt Gödel Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik vol. 38 (1931) pp. 173-198. MR 1549910

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David Hilbert and Paul Bernays Grundlagen der Mathematik, vol. 1, 1934, vol. 2, 1939, Berlin, Springer.

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Leon Henkin The completeness of formal systems, a Thesis at Princeton University accepted in October, 1947. (Abstract appeared on p. 61 of J. Symbolic Logic vol. 13 (1948)). MR 0095120 (20:1626)

[2]

-Completeness in the theory of types, J. Symbolic Logic vol. 15 (1950) pp. 81-91. MR 0036188 (12:70b)

[1]

A. Malcev Untersuchungen aus dem Gebiete der mathematischen Logik, Recueil Mathématique N.S. vol. 1 (1936) pp. 323-336.

[1]

John von Neumann Zur Einführung der transfiniten Zahlen, Acta litterarum ac scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, Sectio scientiarum mathematicarum vol. 1 (1923) pp. 199-208.

[1]

Ilse L. Novak A construction for models of consistent systems, Fund. Math. vol. 37 (1950) pp. 87-110. MR 0041082 (12:791c)

[1]

John G. Kemeny Type theory vs. set theory, a Thesis at Princeton University (1949). (Abstract appeared on p. 78 of J. Symbolic Logic vol. 15 (1950)).

[1]

W. V. Quine Mathematical logic, New York, 1940; second printing, Cambridge, Mass., 1947.

[2]

-Element and number, J. Symbolic Logic vol. 6 (1941) pp. 135-149. MR 0006326 (3:289a)

[1]

J. Barkley Rosser and Hao Wang Non-standard models for formal logics, J. Symbolic Logic vol. 15 (1950) pp. 113-129. MR 0038307 (12:384c)

[1]

Arnold Schmidt Über deduktive Theorien mit mehreren Sorten von Grunddingen, Math. Ann. vol. 115 (1938) pp. 485-506. MR 1513200

[1]

Thoralf Skolem Über einige Grundlagenfragen der Mathematik, Skrifter utgitt av Det. Norske Viden-skaps-Akademi, I, no. 4, 1929, 49 pp.

[2]

-Über die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Aussagen mit ausschliesslich Zahlenvariablen, Fund. Math. vol. 23 (1934) pp. 150-161.

[1]

Alfred Tarski Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philosophica vol. 1 (1936) pp. 261-405. (Original in Polish, 1933.)

[2]

-On undecidable statements in enlarged systems of logic and the concept of truth, J. Symbolic Logic vol. 4 (1939) pp. 105-112. MR 0000210 (1:34c)

[3]

-The semantic conception of truth and the foundations of semantics, Readings in Philosophical Analysis, selected and edited by Herbert Feigl and Wilfred Sellars, New York, 1949, pp. 52-84. (Original appeared in Philosophy and Phenomenological Research vol. 4 (1944).) MR 0010521 (6:31e)

[1]

Hao Wang A new theory of element and number, J. Symbolic Logic vol. 13 (1948) pp. 129-137. MR 0026978 (10:229g)

[2]

-On Zermelo's and von Neumann's axioms for set theory, Proc. Nat. Acad. Sci. U.S.A. vol. 35 (1949) pp. 150-155. MR 0029850 (10:670b)

[3]

-Remarks on the comparison of axiom systems, ibid. vol. 36 (1950) pp. 448-453. MR 0039661 (12:578j)

[4]

-Arithmetic translations of axiom systems, Trans. Amer. Math. Soc. vol. 71 (1951) pp. 283-293. MR 0043046 (13:198p)