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References
P. Bacsich,Primality and model completions, Alg. Univ.3 (1973), 265–270.
J. Baldwin and A. H. Lachlan,On universal Horn classes, Alg. Univ.3 (1973), 98–111.
S. Burris,Separating sets in modular lattices with applications to congruence lattices, Alg. Univ. (to appear).
S. Burris and E. Jeffers,On the simplicity and subdirect irreducibility of Boolean ultrapowers, Preliminary report, Notices Amer. Math. Soc.22 (1975), A-391.
S. Burris and H. P. Sankappanavar,Lattice-theoretic decision problems in universal algebra, Alg. Univ. (to appear).
C. C. Chang and H. J. Keisler,Model Theory, North Holland, 1973.
S. Comer,Elementary properties of structures of sections, Bol. Soc. Mat. Mexicana (to appear).
S. Comer,Arithmetic properties of relatively free products, (Preprint).
A. Day,Injectivity in equational classes of algebras, Canad. J. Math.,24 (1972), 209–220.
Yu. L. Ershov,On the elementary theory of Post varieties, Algebra i Logika 6 (1967), 7–15, (Russian).
S. Feferman and R. L. Vaught,The first-order properties of products of algebraic systems, Fund. Math.47 (1959), 57–103.
A. L. Foster,Generalized ‘Boolean’ theory of universal algebras, part I. Subdirect sums and normal representation theorem. Math. Z.58 (1953), 306–336.
A. L. Foster,Generalized ‘Boolean’ theory of universal algebras, part II. Identies and subdirect sums of functionally complete algebras, Math. Z.59 (1953), 191–199.
G. Fraser and A. Horn,Congruence relations in direct products, Proc. Amer. Math. Soc.26 (1970), 390–394.
M. Gould and G. Grätzer,Boolean extensions and normal subdirect powers of finite universal algebras, Math. Z.99 (1967), 16–25.
G. Grätzer,Universal Algebra, Van Nostrand, 1968.
W. Hanf,On some fundamental problems concerning isomorphism of Boolean algebras, Math. Scand.5 (1957), 205–217.
Tah-Kai Hu,Stone duality for primal algebra theory, Math. Z.110 (1969), 180–198.
A. A. Iskander,On Boolean extensions of primal algebras, Math. Z.124 (1972), 203–207.
P. V. Jugannadham,A characterization of Boolean extension of universal algebras, Math. Ann.172 (1967), 119–123.
B. Jónsson,On isomorphism types of groups and other algebraic systems, Math. Scand.5 (1957), 224–229.
B. Jónsson,On direct decompositions of torsion-free Abelian groups, Math. Scand.5 (1957), 230–235.
B. Jónsson and P. Olin,Elementary equivalence and relatively free products of lattices, Preliminary report, Notices Amer. Math. Soc.21 (1974), A-370.
B. Jónsson and A. Tarski,Direct Decompositions of Finite Algebraic Systems, Notre Dame Math. Lectures #5, 1947.
K. Keimel and H. Werner,Stone duality for varieties generated by quasi-primal algebras, Mem. Amer. Math. Soc.148 (1974), 59–85.
S. Kinoshita,A solution of a problem of R. Sikorski, Fund. Math.40 (1953), 39–41.
R. Kopperman,Model Theory and its Applications, Allyn and Bacon, 1972.
A. Macintyre,Model-completeness for sheaves of structures, (Preprint).
R. Mansfield,The theory of Boolean ultrapowers, Ann. of Math. Logic2 (1971), 297–325.
R. Magari,Una dimonstrazione del fatto che ogni varieta ammettee algebre simplici, Annali dell' Universita di Ferrara (Nuova Serie), Sezione VII, Science Mathematiche, Vol.XIV. N.I.
J. D. Monk and R. M. Solovay,On the number of complete Boolean algebras, Alg. Univ.2 (1972), 365–369.
A. Mostowski,On direct products of theories, J. Symbolic Logic17 (1952), 1–31.
B. H. Neumann and Sadayuki Yamamuro,Boolean powers of simple groups, J. Austral. Math. Soc.5 (1965), 315–324.
P. Olin,Elementary types of free products of Boolean algebras, Preliminary report, Notices Amer. Math. Soc.21 (1974), A-554.
P. Olin,Free products and elementary equivalence, Pac. J. Math.52 (1974), 175–184.
A. I. Omarov,On subsystems of reduced powers, Algebra and Logic12 #1 (1973), 42–46, in the English translation.
R. S. Pierce,Modules over commutative regular rings, Mem. Amer. Math. Soc. No.70 (1967).
R. W. Quackenbush,Free products of bounded distributive lattices, Alg. Univ.2 (1972), 393–394.
M. O. Rabin,Decidability of second-order theories and automata on infinite trees, Trans. Amer. Math. Soc.141 (1969), 1–35.
P. Ribenboim,Boolean Powers, Fund. Math.65 (1969), 243–268.
P. C. Rosenbloom,Post algebras. I: Postulates and general theory, Amer. J. Math.64 (1942), 167–188.
S. Shelah,Every two elementary equivalent models have isomorphic ultrapowers, Israel J. Math.10 (1971), 224–233.
T. Skolem,Untersuchungen über die Axiome des Klassenkalküls und über die Produktations- und Summations probleme, welche gewisse Klassen von Aussagen betreffen, Skrifter utgit av Videskapsselkapet i Kristiania, I Klasse, No. 3, 1919.
N. V. Subrahmanyam,Boolean vector spaces. I., Math. Z.83 (1964), 422–433.
N. V. Subrahmanyam,Boolean vector spaces. II., Math. Z.87 (1965), 401–419.
A. Tarski,Cardinal Algebras, with an appendix by B. Jónsson and A. Tarski,Cardinal Products of Isomorphism Types, New York, 1949.
A. Tarski,Arithmetical classes and types of mathematical systems, mathematical aspects of arithmetical classes and types, arithmetical classes and types of Boolean algebras, arithmetical classes and types of algebraically closed and real-closed fields, Bull. Amer. Math. Soc.55 (1949), 63–64.
A. Tarski,Remarks on direct products of commutative semigroups, Math. Scand.5 (1957), 218–223.
W. Taylor,The fine spectrum of a variety, (Preprint, 1974).
R. L. Vaught,Denumerable models of complete theories, Proceedings of the Symposium in Foundations of Mathematics, Infinitistic Methods, New York 1961, 303–321.
J. Waszkiewicz and B. Weglorz,Some models of theories of reduced powers, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.16 (1968), 683–685.
J. Waszkiewicz and B. Weglorz,On ω 0 of powers, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.17 (1969), 195–199.
B. Weglorz,Equationally compact algebras (I), Fund. Math.59 (1966). 289–298.
B. Weglorz,Limit generalized powers, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astonom. Phys.16 (1968), 449–451.
B. Weglorz,Some remarks on reduced powers, (Abstract) J. Symbolic Logic39 (1974), p. 387.
H. Werner,Congruences on products of algebras and functionally complete algebras, Alg. Univ.4 (1974), 99–105.
A. Wojciechowska,Generalized limit powers, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.17 (1969), 121–122.
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Research supported by NRC Grant A7256.
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Burris, S. Boolean powers. Algebra Universalis 5, 341–360 (1975). https://doi.org/10.1007/BF02485268
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DOI: https://doi.org/10.1007/BF02485268