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Generalization of the concept of variety and quasivariety to partial algebras through category theory

Autorzy

H. Andréka I. Németi

Seria

Rozprawy Matematyczne tom/nr w serii: 204 wydano: 1983

Zawartość

Pełne teksty:
rm20401.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS
Introduction ................................................................................................5
§1. The purely category theoretical version of Birkhoff's theorem................7
§2. Category theoretical study of generalized identities............................19
§3. Generalized identities in partial algebras.............................................29
§4. Calculus...............................................................................................41
§5. Examples.............................................................................................47
§6. Some model-theoretic consequences.................................................48
References...............................................................................................50

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 204

Liczba stron

51

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Opis fizyczny

Dissertationes Mathematicae, Tom CCIV

Daty

wydano
1983

Twórcy

autor
H. Andréka
autor
I. Németi

Bibliografia

  • [1] H. Andréka, T. Gergely, I. Németi, On universal algebraic construction of logics, KFKI-74-41, 1974. Also in: Studia Logica 36 (1977) 1-2, pp. 9-47.
  • [2] H. Andréka, T. Gergely, I. Németi, Easily comprehensible mathematical logic and its model theory, KFKI-75-24, 1975.
  • [3] H. Andréka, I. Németi, Formulas and ultraproducts in categories. Beiträge Algebra und Geometrie 8 (1979), pp. 133-151.
  • [4] H. Andréka, I. Németi, A general axiomatizability theorem formulated in terms of cone-injective subcategories, in: Contributions to Universal Algebra (Proc. Coll. Esztergom 1977). Coll. Math. Soc. J. Bolyai vol. 29, North-Holland, 1981, pp. 13-35.
  • [5] H. Andréka, I. Németi, Injectivity in categories to represent all first order formulas, Demonstratio Math. 12 (1979), pp. 717-732.
  • [6] H. Andréka, I. Németi, Loś-lemma holds in every category, Studia Sci. Math. Hungar. 13 (1978), pp. 361-376.
  • [7] H. Andréka, I. Németi, On the more general notion of factorization systems, Periodica Math. Hungar. 13 (1981).
  • [8] B. Banaschewski, H. Herrlich, Subcategories defined by implications. Houston J. Math. 2, 2 (1976), pp. 149-171.
  • [9] J. Barwise, Axioms for abstract model theory, Annals Math. Logic 7 (1974).
  • [10] J. Barwise, Back and forth through infinitary logic, MAA Studies # 8, Studies in model theory (ed. M. Morley), 1975.
  • [11] V. Bauman, J. Pfanzagl, The closure operator in partial algebras with distributive operations. Math. Z. 92 (1966).
  • [12] G. Birkhoff, On the structure of abstract algebras, Proc. Cambridge Philos. Soc. 31 (1935).
  • [13] P. Burmeister, Partial algebras. Survey of a unifying approach towards a two-valued model theory for partial algebras, Algebra Universalis, to appear.
  • [14] P. Burmeister, R. John, A. Pasztor, On closed morphisms in the category of partial algebras. Contributions to General Algebra, Proc. Conf. Klagenfurt 1978, Verlag J. Heyn.
  • [15] C. C. Chang, H. J. Keisler, Model theory, North-Holland, 1973.
  • [16] G. A. Edgar, The class of topological spaces is equationally definable. Algebra Universalis, 1973.
  • [17] T. Gergely, I. Németi, A. Pasztor, The concept of variety in the theory of categories, KFKI-75-60, 1975.
  • [18] G. Grätzer, Universal algebra, Van Nostrand, 1968, Revised edition Springer-Verlag, 1979.
  • [19] L. Henkin, J. D. Monk, A. Tarski, Cylindric algebras, North-Holland, 1971.
  • [20] H. Herrlich, C. M. Ringel, Identities in categories, Canad. Math. Bull. 12/2 (1972), pp. 297-299.
  • [21] H. Herrlich, G. E. Strecker, Category theory, Allyn and Bacon, 1973.
  • [22] H. Höft, Operators on classes of partial algebras, Algebra Universalis 2 (1972).
  • [23] H. Höft, Weak and strong equations in partial algebra, Algebra Universalis 3 (1973).
  • [24] J. R. Isbell, Normal completions of categories, Reports Midwest Category Seminar, Lecture Notes in Math. vol. 47, Springer-Verlag, 1967, pp. 110-155.
  • [25] R. John, Gültigkeitsbegriffe für Gleichungen in Partiellen Algebren, Technische Hochschule Darmstadt, Preprint 250 (1976).
  • [26] S. MacLane, Categories for the working mathematician, Springer-Verlag, 1971.
  • [27] A. I. Malcev, The metamathematics of algebraic systems, North-Holland, 1971.
  • [28] G. Matthiessen, Regular and strongly finitary structures over strongly algebroidal categories, Canad. J. Math. 30 (1978), pp. 250-261.
  • [29] B. Mitchell, Theory of categories, Academic Press, 1965.
  • [30] F. E. J. Linton, An outline of functorial semantics, Lecture Notes in Math. vol. 80, Springer-Verlag. 1969. pp. 7 52.
  • [31] I. Németi, From hereditary classes to varieties in abstract model theory and partial algebra, Beiträge Algebra und Geometrie 7 (1978), pp. 69-78.
  • [32] I. Németi, I. Sain, Cone-injectivity and some Birkhoff type theorems in categories, in: Contributions to Universal Algebra (Proc. Coll. Esztergom 1977) Coll. Math. Soc. J. Bolyai vol. 29, North-Holland, 1981, pp. 535 -578.
  • [33] I. Németi, I. Sain, Connections between algebraic logic and initial algebra semantics of CF languages, in: Mathematical Logic in Computer sciences (Proc. Coll. Solgótarjān 1978) Coll. Math. Soc. J. Bolyai vol. 26, North-Holland, 1981. Part I, pp. 25-83; Part II, pp. 261-605.
  • [34] A. Pasztor, Generalizing identities to partial algebras through category theory, Master theses, Eötvös Lóránd University Budapest, May 1974.
  • [35] A. Pasztor, A characterization of surjections in the category of partial algebras, Studia Sci. Math. Hungar. 12 (1977), pp. 251-256.
  • [36] A. Pasztor, Faktorisierungssysteme in der Kategorie der Partiellen Algebren, Kennzeichnung von (Homo) Morphismenklassen, Hochschul Verlag, Freiburg 1979, p. 115.
  • [37] I. Sain, Category theoretical investigations in order to generalize identities and quasi-identities, e.g. to partial algebras, Master theses, Eötvös Lórānd University Budapest, May 1974.
  • [38] I. Sain, On classes of algebraic systems closed w.r.t. quotients, To appear in Banach Center Publications 9, Universal algebra and applications.
  • [39] J. Schmidt, A homomorphism theorem for partial algebras, Coll. Math. 21 (1970).
  • [40] A. Selman, Completeness of calculi for axiomatically defined classes of algebras, Algebra Universalis 2 (1972).
  • [41] A. Shafaat, On implicationally defined classes of algebras, London Math. Soc. (1969).
  • [42] J. Słomiński, Peano-algebras and quasi-algebras, Diss. Math. 57 (1968).
  • [43] B. Wojdyło, Categories of quasi-algebras, Inst. Math. N. Copernicus Univ. Toruń, Preprint 2 (1972).

Języki publikacji

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Identyfikator YADDA

bwmeta1.element.zamlynska-501e312d-2b1c-4691-92a6-a3af4587bbea

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ISBN
83-01-02220-5
ISSN
0012-3862

Kolekcja

DML-PL
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