Amalgamation of polyadic algebras
HTML articles powered by AMS MathViewer
- by James S. Johnson PDF
- Trans. Amer. Math. Soc. 149 (1970), 627-652 Request permission
Abstract:
The main result of the paper is that for I an infinite set, the class of polyadic I-algebras (with equality) has the strong amalgamation property; i.e., if two polyadic I-algebras have a given common subalgebra they can be embedded in another algebra in such a way that the intersection of the images of the two algebras is the given common subalgebra.References
-
S. Comer, Some representation theorems and the amalgamation property in algebraic logic, Doctoral Dissertation, University of Colorado, Boulder, 1967.
- Aubert Daigneault, On automorphisms of polyadic algebras, Trans. Amer. Math. Soc. 112 (1964), 84–130. MR 162741, DOI 10.1090/S0002-9947-1964-0162741-6
- Aubert Daigneault, Freedom in polyadic algebras and two theorems of Beth and Craig, Michigan Math. J. 11 (1964), 129–135. MR 166130 —, Théorie des modèles en logique mathématique, Séminaire de mathématiques supérieures, Université de Montréal, 1963.
- A. Daigneault and D. Monk, Representation theory for polyadic algebras, Fund. Math. 52 (1963), 151–176. MR 151373, DOI 10.4064/fm-52-2-151-176
- T. Frayne, A. C. Morel, and D. S. Scott, Reduced direct products, Fund. Math. 51 (1962/63), 195–228. MR 142459, DOI 10.4064/fm-51-3-195-228 G. Grätzer, Universal algebra, University Series in Higher Mathematics, Van Nostrand, Princeton, N. J., 1968.
- P. R. Halmos, Algebraic logic. II. Homogeneous locally finite polyadic Boolean algebras of infinite degree, Fund. Math. 43 (1956), 255–325. MR 86029
- Paul R. Halmos, Algebraic logic. IV. Equality in polyadic algebras, Trans. Amer. Math. Soc. 86 (1957), 1–27. MR 90564, DOI 10.1090/S0002-9947-1957-0090564-1 —, Algebraic logic, Chelsea, New York, 1962. MR 24 #A1808. L. Henkin, D. Monk and A. Tarski, Cylindric algebras. Vol. I, North-Holland, Amsterdam, (to appear).
- Leon Henkin and Alfred Tarski, Cylindric algebras, Proc. Sympos. Pure Math., Vol. II, American Mathematical Society, Providence, R.I., 1961, pp. 83–113. MR 0124250 J. S. Johnson, Amalgamation of polyadic algebras, Abstract #644-8, Notices Amer. Math. Soc. 14 (1967), 361.
- H. J. Keisler, A complete first-order logic with infinitary predicates, Fund. Math. 52 (1963), 177–203. MR 152419, DOI 10.4064/fm-52-2-177-203
- Helena Rasiowa and Roman Sikorski, The mathematics of metamathematics, Monografie Matematyczne, Tom 41, Państwowe Wydawnictwo Naukowe, Warsaw, 1963. MR 0163850
- Roman Sikorski, Boolean algebras, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 25, Academic Press, Inc., New York; Springer-Verlag, Berlin-New York, 1964. MR 0177920
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 149 (1970), 627-652
- MSC: Primary 02.48
- DOI: https://doi.org/10.1090/S0002-9947-1970-0284319-9
- MathSciNet review: 0284319