Properties preserved under algebraic constructions
R. C. Lyndon
Source: Bull. Amer. Math. Soc. Volume 65, Number 5
(1959), 287-299.
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Permanent link to this document: http://projecteuclid.org/euclid.bams/1183523309
Mathematical Reviews number (MathSciNet): MR0111687
Zentralblatt MATH identifier: 0087.00903
References
K. I. Appel, 1958. Horn sentences in identity theory, Notices Amer. Math. Soc. vol. 6, p. 343.
Zentralblatt MATH: 0114.24502
Mathematical Reviews (MathSciNet): MR132691
Digital Object Identifier: doi:10.2307/2963901
E. W. Beth, 1953. On Padoa's method in the theory of definition, Indag. Math. vol. 15, p. 66.
Zentralblatt MATH: 0051.00601
Mathematical Reviews (MathSciNet): MR53043
K. Bing, 1955. On arithmetical classes not closed under direct union, Proc. Amer. Math. Soc. vol. 6, p. 836.
Zentralblatt MATH: 0068.24701
Mathematical Reviews (MathSciNet): MR72086
Digital Object Identifier: doi:10.1090/S0002-9939-1955-0072086-0
G. Birkhoff, 1935. On the structure of abstract algebras, Proc. Cambridge Philos. Soc. vol. 31, p. 433.
Zentralblatt MATH: 0013.00105
C. C. Chang, 1956. On the unions of chains of models, Bull. Amer. Math. Soc. vol. 62, p. 598.
Zentralblatt MATH: 0096.24205
C. C. Chang, 1959. On unions of chains of models, Proc. Amer. Math. Soc. vol. 10, p. 120.
Zentralblatt MATH: 0096.24205
Mathematical Reviews (MathSciNet): MR103812
Digital Object Identifier: doi:10.1090/S0002-9939-1959-0103812-3
C. C. Chang and A. C. Davis (Morel), 1956. Arithmetical classes closed under direct product, Bull. Amer. Math. Soc. vol. 62, p. 411.
C. C. Chang and A. C. Morel, 1958. On closure under direct product, J. Symb. Logic vol. 23, p. 149.
Zentralblatt MATH: 0092.00603
Mathematical Reviews (MathSciNet): MR104606
Digital Object Identifier: doi:10.2307/2964395
W. Craig, 1957a. Linear reasoning. A new form of the Herbrand-Gentzen theorem, J. Symb. Logic vol. 22, p. 250.
Zentralblatt MATH: 0081.24402
Mathematical Reviews (MathSciNet): MR104564
Digital Object Identifier: doi:10.2307/2963593
W. Craig, 1957b. Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory, J. Symb. Logic vol. 22, p. 269.
Zentralblatt MATH: 0079.24502
Mathematical Reviews (MathSciNet): MR104565
Digital Object Identifier: doi:10.2307/2963594
T. E. Frayne, D. S. Scott and A. Tarski, 1958. Reduced products, Notices Amer. Math. Soc. vol. 5, p. 673.
L. Henkin, 1953. Some interconnections between modern algebra and mathematical logic, Trans. Amer. Math. Soc. vol. 74, p. 410.
Zentralblatt MATH: 0050.00603
Mathematical Reviews (MathSciNet): MR55287
Digital Object Identifier: doi:10.1090/S0002-9947-1953-0055287-X
L. Henkin, 1956. Two concepts from the theory of models, J. Symb. Logic vol. 21, p. 28.
Zentralblatt MATH: 0071.00701
Mathematical Reviews (MathSciNet): MR75895
Digital Object Identifier: doi:10.2307/2268482
A. Horn, 1951. On sentences which are true of direct unions of algebras, J. Symb. Logic vol. 16, p. 14.
Zentralblatt MATH: 0043.24801
Mathematical Reviews (MathSciNet): MR40233
Digital Object Identifier: doi:10.2307/2268661
P. Jordan, 1949. Zur Axiomatik der Verknüpfungsbereiche, Abh. Math. Sem. Univ. Hamburg vol. 16, p. 54.
Zentralblatt MATH: 0037.15602
Mathematical Reviews (MathSciNet): MR30933
Digital Object Identifier: doi:10.1007/BF02941086
C. R. Karp, 1958. Formalizations of functional languages with wffs of infinite length, Notices Amer. Math. Soc. vol. 5, p. 172.
H. J. Keisler, 1958. The theory of models with generalized atomic formulas, I and II, Notices Amer. Math. Soc. vol. 5, pp. 676, 621.
Zentralblatt MATH: 0107.00803
S. Kochen, 1958. Filtration systems, I and II, Notices Amer. Math. Soc. vol. 5, pp. 67, 671.
J. Łoś, 1955a. On the extending of models, I, Fund. Math. vol. 42, p. 38.
Zentralblatt MATH: 0065.00401
Mathematical Reviews (MathSciNet): MR72071
J. Łoś, 1955b. Quelques remarques, théorèmes et problèmes sur les classes définissables d'algèbres, Studies in Logic and Foundations of Mathematics, North Holland, Amsterdam, p. 98.
Zentralblatt MATH: 0068.24401
J. Łoś and R. Suszko, 1955. On the infinite sum of models, Bull. Acad. Polon. Sci. Cl. III vol. 3, p. 201.
Zentralblatt MATH: 0066.25504
Mathematical Reviews (MathSciNet): MR72072
R. C. Lyndon, 1951. Review of Horn, 1951, J. Symb. Logic vol. 16, p. 216.
R. C. Lyndon, 1957a. On positive formulas in the predicate logic, Bull. Amer. Math. Soc. vol. 63, p. 282.
R. C. Lyndon, 1957b. On positive classes of relational systems and algebras, Bull. Amer. Math. Soc. vol. 63, p. 282.
R. C. Lyndon, 1957c. On special Horn sentences, Bull. Amer. Math. Soc. vol. 63, p. 356.
R. C. Lyndon, 1957d. On subdirect products of relational systems, Bull. Amer. Math. Soc. vol. 63, p. 356.
R. C. Lyndon, 1958a. A semantic Herbrand-Gentzen lemma, Notices Amer. Math. Soc. vol. 5, p. 464.
R. C. Lyndon, 1958b. Direct products of algebras, Notices Amer. Math. Soc. vol. 5, p. 848.
R. C. Lyndon, 1959a. An interpolation theorem in the predicate calculus, Pacific J. Math. vol. 9, p. 129.
Zentralblatt MATH: 0093.01002
Mathematical Reviews (MathSciNet): MR106825
Project Euclid: euclid.pjm/1103039458
R. C. Lyndon, 1959b. Properties preserved under homomorphism, Pacific J. Math. vol. 9, p. 143.
Zentralblatt MATH: 0093.01101
Mathematical Reviews (MathSciNet): MR108441
Project Euclid: euclid.pjm/1103039459
R. C. Lyndon, 1959c. Properties preserved in subdirect products, Pacific J. Math. vol. 9, p. 155.
Zentralblatt MATH: 0093.01102
Mathematical Reviews (MathSciNet): MR107606
Project Euclid: euclid.pjm/1103039460
R. C. Lyndon, Existential Horn sentences, to appear in Proc. Amer. Math. Soc.
Zentralblatt MATH: 0114.24902
Mathematical Reviews (MathSciNet): MR115914
Digital Object Identifier: doi:10.1090/S0002-9939-1959-0115914-6
A. I. Malcev, 1956. Subdirect products of models, Dokl. Akad. Nauk SSSR vol. 109, p. 264.
Mathematical Reviews (MathSciNet): MR86770
E. Marczewski, 1951. Sur les congruences et les propriétés positives d'algèbres abstraites, Colloq. Math. vol. 2, p. 220.
Zentralblatt MATH: 0045.00105
Mathematical Reviews (MathSciNet): MR50564
J. C. C. McKinsey, 1943. The decision problem for some classes of sentences without quantifiers, J. Symb. Logic vol. 8, p. 61.
Zentralblatt MATH: 0063.03864
Mathematical Reviews (MathSciNet): MR8991
Digital Object Identifier: doi:10.2307/2268172
A. C. Morel, D. S. Scott and A. Tarski, 1958. Reduced products and the compactness theorem, Notices Amer. Math. Soc. vol. 5, p. 674.
A. Oberschelp, 1958. Über die Axiome produkt-abgeschlossener arithmetischer Klassen, Archiv für Math. Logik und Grundlagenforschung vol. 4, p. 95.
Zentralblatt MATH: 0108.00601
Mathematical Reviews (MathSciNet): MR107605
Digital Object Identifier: doi:10.1007/BF01973146
A. Robinson, 1950. On the metamathematics of algebra, Studies in Logic and Foundations of Mathematics, North Holland, Amsterdam.
Zentralblatt MATH: 0043.24702
Mathematical Reviews (MathSciNet): MR46322
A. Robinson, 1956. Note on a problem of Henkin, J. Symb. Logic vol. 21, p. 33.
Zentralblatt MATH: 0071.00702
Mathematical Reviews (MathSciNet): MR75896
Digital Object Identifier: doi:10.2307/2268483
A. Seidenberg, 1958. Comments on Lefschetz's Principle, Amer. Math. Monthly vol. 65, p. 685.
Zentralblatt MATH: 0108.16903
Mathematical Reviews (MathSciNet): MR98746
Digital Object Identifier: doi:10.2307/2308709
A. Tarski, 1950. Some notions and methods on the borderline of algebra and metamathematics, Proceedings of the International Congress of Mathematicians, Cambridge, vol. 1, p. 705.
Zentralblatt MATH: 0049.00702
Mathematical Reviews (MathSciNet): MR45068
A. Tarski, 1954. Contributions to the theory of models, I and II, Indag. Math. vol. 16, pp. 572, 582.
Zentralblatt MATH: 0058.24702
Mathematical Reviews (MathSciNet): MR66301
A. Tarski, 1958. Some model-theoretic results concerning weak second-order logic, Notices Amer. Math. Soc. vol. 5, p. 673.
A. Tarski and R. L. Vaught, 1957. Arithmetical extensions of relational systems, Compositio Math. vol. 13, p. 81.
Zentralblatt MATH: 0091.01201
Mathematical Reviews (MathSciNet): MR95121
R. L. Vaught, 1954. On sentences holding in direct products of relational systems, Proceedings of the International Congress of Mathematicians, Amsterdam, vol. 2, p. 409.
R. G. Zubieta, 1957. Clases matematicas definadas sin igualdad, Bol. Soc. Mat. Mex. vol. 2, p. 45.
Mathematical Reviews (MathSciNet): MR95771
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