This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J. Adamek, E. Nelson, J. Reiterman: "Tree Construction of Free Continuous Algebras", J. Comp. Syst. Sciences 24 (1982), 114–146.
J. Adamek, E. Nelson, J. Reiterman: "The Birkhoff Variety Theorem for Continuous Algebras", Preprint, 1984.
ADJ (= J.A. Goguen, J.W. Thatcher, E.G. Wagner, and J.B. Wright), "Some fundamentals of order-algebraic semantics", in Proc. Symp. Math. Found. of Comp. Sci., Gdansk, Poland, Sept. 1976, Springer-Verlag Lecture Notes in Computer Science (1976), 153–168.
ADJ, "Initial algebra semantics and continuous theories", J. Assoc. Comput. Mach. 24 (1977), 68–95.
ADJ, "Free Continuous Theories", IBM Res. Repart 6909, Yorktown Heights (1977).
ADJ, "An initial algebra approach to the specification, correctness and implementation of abstract data types", Current Trends in Programming Methodology 3, Data Structuring, R.T. Yeh, ed., Prentice Hall (1977).
H. Andreka, P. Burmeister, I. Nemeti, "Quasivarieties of partial algebras — a unifying approach towards a two-valued model theory for partial algebras", to appear in Studia Sci. Math. Hungar.
H. Andreka, I. Nemeti, "Generalization of variety and quasivariety concept to partial algebras through category theory", preprint Math. Inst. Hungar. Acad. Sci. (1976), and Dissertationes Mathem. (Rozprawy Math.) 204, PWN-Polish Scientific Publishers, Warsaw (1982), 1–56.
H. Andreka, I. Nemeti, "A general axiomatizability theorem formulated in terms of cone-injective subcategories", Universal Algebra (Proc. Coll. Esthergom 77), Colloq. Math. Soc. J. Bolyai 29 (1981), 13–35.
H. Andreka, I. Nemeti: "Applications of universal algebra, model theory, and categories in computer science". (Survey and bibliography.) Parts I–III, Part I in CL & CL 13 (1979), 152–282. Part II in CL & CL 14 (1980), 7–20. Part III ("Some universal algebraic and model theoretic results in computer science") in: Fundamentals of Computation Theory (Szeged 1981) Springer-Verlag, Lecture Notes in Computer Science 117 (1981), 16–23.
H. Andreka, I. Nemeti: "Injectivity in categories to represent all first order formulas". Demonstratio Mathematicae 12 (1979), 717–732.
H. Andreka, I. Nemeti: "Los lemma holds in every category". Studia Sci. Math. Hungar. 13 (1978), 361–376.
B. Banaschewski, H. Herrlich: "Subcategories defined by implications", Houston J. Math. 2 (1976), 149–171.
S.L. Bloom, "Varieties of ordered algebras", J. Comp. & Systems Sci. 13 (1976), 200–212.
P. Burmeister, "Partial algebras — survey of a unifying approach towards a two-valued model theory for partial algebras", Algebra Universalis 15 (1982), 306–358.
B. Courcelle, M. Nivat: "Algebraic families of interpretations", 17th IEEE Symp. FOCS (1976), 137–146.
J.H. Gallier, "n-Rational Algebras. Part I: Basic Properties and Free Algebras; Part II: Varieties and Logic of Inequalities", to appear in SIAM On Computing.
I. Guessarian, "Algebraic Semantics", Springer-Verlag, Lecture Notes in Computer Science 99 (1981).
I. Guessarian, "Survey on classes of interpretations and some of their applications", Laboratoire informatique theorique et programmation — Report 82–46, October, 1982.
H. Herrlich, G.E. Strecker, "Category Theory", Allyn and Bacon, Inc., Boston (1973).
B.H. Hien, I. Sain: "Elementary classes in the injective subcategories approach to abstract model theory". Preprint, Math. Inst. Hungar. Acad. Sci. 15 (1982).
D. Lehmann, "On the algebra of order", J. Comp. Systems Sci. 21/1 (1980), 1–23.
A.I. Mal'cev:"Algebraic Systems", Springer Verlag (1973).
A.I. Mal'cev:"The Metamathematics of Algebraic Systems", North Holland (1971).
J. Meseguer, "On order-complete universal algebra and enriched functorial semantics", Springer-Verlag, Lecture Notes in Computer Science 56 (1977), 294–301.
J. Meseguer, "A Birkhoff-like theorem for algebraic classes of interpretations of program schemes", Springer-Verlag, Lecture Notes in Computer Science 107 (1981), 152–168.
J. Meseguer:"Varieties of chain-complete algebras". J. Pure Appl. Algebra 19 (1980), 347–383.
E. Nelson, "Free Z-continuous algebras", Springer-Verlag, Lecture Notes in Mathematics 871 (1981), 315–334.
I. Nemeti, I. Sain, "Cone-implicational subcategories and some Birkhoff-type theorems", Universal Algebra (Proc. Coll. Esztergom 1977), Colloq. Math. Soc, J. Bolyai 29, North-Holland (1981), 535–578.
I. Nemeti:"On notions of factorization systems and their applications to cone-injective subcategories". Periodica Math. Hungar. 13/3 (1982), 229–235.
A. Pasztor, "Chain-continuous algebras — a variety of partial algebras", in Fundamenta Informatica vi/3–4 (1983), 275–288.
I. Sain, B.H. Hien, "In which categories are first order axiomatizable hulls characterizable by ultra products". Cahiers Top. Geom. Diff. xxiv–2 (1983), 215–222.
D. Scott, "Outline of a math. theory of computation", in Proc. 4th Ann. Princeton Conf. on Inf. Sci. & Systems (1969), 169–176.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pasztor, A. (1986). On the variety concept for ω-continuous algebras. Application of a general approach. In: Melton, A. (eds) Mathematical Foundations of Programming Semantics. MFPS 1985. Lecture Notes in Computer Science, vol 239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16816-8_35
Download citation
DOI: https://doi.org/10.1007/3-540-16816-8_35
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16816-4
Online ISBN: 978-3-540-44861-7
eBook Packages: Springer Book Archive