Arbitrarily large continuous algebras on one generator

Adámek, Jiří; Koubek, Václav; Nelson, Evelyn; Reiterman, Jan

doi:10.1090/S0002-9947-1985-0800258-7

Arbitrarily large continuous algebras on one generator
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by Jiří Adámek, Václav Koubek, Evelyn Nelson and Jan Reiterman PDF

Trans. Amer. Math. Soc. 291 (1985), 681-699 Request permission

Abstract:

Generation of order-continuous algebras is investigated for various concepts of continuity. For the continuity understood as the preservation of joins of countably-directed sets, arbitrarily large infinitary continuous algebras on one generator are constructed.

References

Jiří Adámek, Colimits of algebras revisited, Bull. Austral. Math. Soc. 17 (1977), no. 3, 433–450. MR 470020, DOI 10.1017/S0004972700010704
Jiří Adámek, Construction of free continuous algebras, Algebra Universalis 14 (1982), no. 2, 140–166. MR 634995, DOI 10.1007/BF02483917
Jiří Adámek and Evelyn Nelson, Separately continuous algebras, Theoret. Comput. Sci. 27 (1983), no. 1-2, 225–231. MR 742287, DOI 10.1016/0304-3975(83)90102-0
Jiří Adámek, Evelyn Nelson, and Jan Reiterman, Tree constructions of free continuous algebras, J. Comput. System Sci. 24 (1982), no. 1, 114–146. MR 645852, DOI 10.1016/0022-0000(82)90059-9
J. B. Wright, E. G. Wagner, and J. W. Thatcher, A uniform approach to inductive posets and inductive closure, Theoret. Comput. Sci. 7 (1978), no. 1, 57–77. MR 480224, DOI 10.1016/0304-3975(78)90040-3
Bernhard Banaschewski and Evelyn Nelson, Completions of partially ordered sets, SIAM J. Comput. 11 (1982), no. 3, 521–528. MR 664718, DOI 10.1137/0211041
J. E. Baumgartner, Ineffability properties of cardinals. I, Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I, Colloq. Math. Soc. János Bolyai, Vol. 10, North-Holland, Amsterdam, 1975, pp. 109–130. MR 0384553
N. Bourbaki, Éléments de mathématique. 22. Première partie: Les structures fondamentales de l’analyse. Livre 1: Théorie des ensembles. Chapitre 4: Structures, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1258, Hermann, Paris, 1957 (French). MR 0097335
Horst Herrlich and George E. Strecker, Category theory: an introduction, Allyn and Bacon Series in Advanced Mathematics, Allyn and Bacon, Inc., Boston, Mass., 1973. MR 0349791
A. Kanamori and M. Magidor, The evolution of large cardinal axioms in set theory, Higher set theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1977) Lecture Notes in Math., vol. 669, Springer, Berlin, 1978, pp. 99–275. MR 520190

Free

-continuous algebras

A. Pasztor, Epis of some categories of $Z$-continuous partial algebras, Acta Cybernet. 6 (1983), no. 1, 111–123. MR 699819