Bulletin of the American Mathematical Society

Properties preserved under algebraic constructions

R. C. Lyndon

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. Volume 65, Number 5 (1959), 287-299.

Dates
First available: 4 July 2007

Permanent link to this document
http://projecteuclid.org/euclid.bams/1183523309

Mathematical Reviews number (MathSciNet)
MR0111687

Zentralblatt MATH identifier
0087.00903

Citation

Lyndon, R. C. Properties preserved under algebraic constructions. Bulletin of the American Mathematical Society 65 (1959), no. 5, 287--299. http://projecteuclid.org/euclid.bams/1183523309.


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References

  • K. I. Appel, 1958. Horn sentences in identity theory, Notices Amer. Math. Soc. vol. 6, p. 343.
  • E. W. Beth, 1953. On Padoa's method in the theory of definition, Indag. Math. vol. 15, p. 66.
  • K. Bing, 1955. On arithmetical classes not closed under direct union, Proc. Amer. Math. Soc. vol. 6, p. 836.
  • G. Birkhoff, 1935. On the structure of abstract algebras, Proc. Cambridge Philos. Soc. vol. 31, p. 433.
  • C. C. Chang, 1956. On the unions of chains of models, Bull. Amer. Math. Soc. vol. 62, p. 598.
  • C. C. Chang, 1959. On unions of chains of models, Proc. Amer. Math. Soc. vol. 10, p. 120.
  • 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.
  • W. Craig, 1957a. Linear reasoning. A new form of the Herbrand-Gentzen theorem, J. Symb. Logic vol. 22, p. 250.
  • W. Craig, 1957b. Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory, J. Symb. Logic vol. 22, p. 269.
  • 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.
  • L. Henkin, 1956. Two concepts from the theory of models, J. Symb. Logic vol. 21, p. 28.
  • A. Horn, 1951. On sentences which are true of direct unions of algebras, J. Symb. Logic vol. 16, p. 14.
  • P. Jordan, 1949. Zur Axiomatik der Verknüpfungsbereiche, Abh. Math. Sem. Univ. Hamburg vol. 16, p. 54.
  • 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.
  • 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.
  • 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.
  • J. Łoś and R. Suszko, 1955. On the infinite sum of models, Bull. Acad. Polon. Sci. Cl. III vol. 3, p. 201.
  • 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.
  • R. C. Lyndon, 1959b. Properties preserved under homomorphism, Pacific J. Math. vol. 9, p. 143.
  • R. C. Lyndon, 1959c. Properties preserved in subdirect products, Pacific J. Math. vol. 9, p. 155.
  • R. C. Lyndon, Existential Horn sentences, to appear in Proc. Amer. Math. Soc.
  • A. I. Malcev, 1956. Subdirect products of models, Dokl. Akad. Nauk SSSR vol. 109, p. 264.
  • E. Marczewski, 1951. Sur les congruences et les propriétés positives d'algèbres abstraites, Colloq. Math. vol. 2, p. 220.
  • J. C. C. McKinsey, 1943. The decision problem for some classes of sentences without quantifiers, J. Symb. Logic vol. 8, p. 61.
  • 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.
  • A. Robinson, 1950. On the metamathematics of algebra, Studies in Logic and Foundations of Mathematics, North Holland, Amsterdam.
  • A. Robinson, 1956. Note on a problem of Henkin, J. Symb. Logic vol. 21, p. 33.
  • A. Seidenberg, 1958. Comments on Lefschetz's Principle, Amer. Math. Monthly vol. 65, p. 685.
  • 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.
  • A. Tarski, 1954. Contributions to the theory of models, I and II, Indag. Math. vol. 16, pp. 572, 582.
  • 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.
  • 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.