On the failure of Birkhoff's theorem for locally small based equational categories of algebras
Herrlich, Horst
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 34 (1993), p. 185-192 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1993-01-01
@article{CTGDC_1993__34_3_185_0,
     author = {Herrlich, Horst},
     title = {On the failure of Birkhoff's theorem for locally small based equational categories of algebras},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {34},
     year = {1993},
     pages = {185-192},
     mrnumber = {1239467},
     zbl = {0797.08006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_1993__34_3_185_0}
}

Herrlich, Horst. On the failure of Birkhoff's theorem for locally small based equational categories of algebras. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 34 (1993) pp. 185-192. http://gdmltest.u-ga.fr/item/CTGDC_1993__34_3_185_0/

[1] J. Adámek, H. Herrlich and G.E. Strecker, Abstract and Concrete Categories, Wiley 1990 | MR 1051419 | Zbl 0695.18001

[2] B. Banaschewski and H. Herrlich, Subcategories defined by implications, Houston J. Math 2 (1976) 149-171 | MR 401867 | Zbl 0344.18002

[3] G. Birkhoff, On the structure of abstract algebras, Proc. Cambr. Phil. Soc. 31 (1935) 433-454 | JFM 61.1026.07

[4] H. Gaifman, Infinite Boolean polynomicals I, Fund. Math. 54 (1964) 230-250 | MR 168503 | Zbl 0126.26404

[5] O. Garcia and E. Nelson, On the non-existence of free complete distributive lattices, Order 1 (1985) 399-403 | MR 787551 | Zbl 0558.06012

[6] A.W. Hales, On the non-existence of free complete Boolean algebras, Fund. Math. 54 (1964) 45-66 | MR 163863 | Zbl 0119.26003

[7] H. Herrlich, Remarks on categories of algebras defined by a proper class of operations, Quaestiones Math. 13 (1990) 385-393 | MR 1084749 | Zbl 0733.18004

[8] J.R. Isbell, A note on complete closure algebras, Math. Syst. Theory 3 (1970) 310-312 | MR 252296 | Zbl 0182.34303

[9] J.R. Isbell, General functorial semantics I, Amer. J. Math. 94 (1972) 535-596 | MR 396718 | Zbl 0439.18009

[10] V. Kŭrková-Pohlová and V. Koubek, When a generalized algebraic category is monadic, Comment. Math. Univ. Carolinae 15 (1974) 577-587 | MR 360743 | Zbl 0294.18004

[11] F.E.J. Linton, Some aspects of equational categories, Proc. Conf. Cat. Algebra, La Jolla 1965, Springer 1966, 84-94 | MR 209335 | Zbl 0201.35003

[12] E.G. Manes, Algebraic Theories, Springer 1976 | MR 419557 | Zbl 0353.18007

[13] J. Reiterman, Large algebraic theories with small algebras, Bull. Austral. Math. Soc. 19 (1978) 371-380 | MR 536889 | Zbl 0401.18003

[14] J. Reiterman, One more categorical model of universal algebra, Math. Z. 161 (1978) 137-146 | MR 498325 | Zbl 0363.18007

[15] J. Reiterman, Structure-semantics relation for non-varietal equational theories, Alg. Univ. 10 (1980)8 399-401 | MR 564124 | Zbl 0444.18004

[16] J. Reiterman, The Birkhoff theorem for finite algebras, Alg. Univ. 14 (1982) 1-10 | MR 634411 | Zbl 0484.08007

[17] J. Reiterman, Algebraic theories and varieties of functor algebras, Fund. Math. 118 (1983) 59-68 | MR 736288 | Zbl 0529.18005

[18] J. Reiterman, On locally small based algebraic theories, Comment. Math. Univ. Carolinae 27 (1986) 325-340 | MR 857552 | Zbl 0598.18003

[19] J. Rosický, On algebraic categories, Coll. Math. Soc. J. Bolyai 29, Univ. Algebra, Erztergom 1977, 663-690 | MR 660901 | Zbl 0495.18005

[20] J. Rosický, Equational categories, Cahiers Topol. Geom. Diff. 22 (1981) 85-95 | Numdam | MR 609163 | Zbl 0463.18002

[21] J Rosický, Varieties of infinitary universal algebras, Alg. Univ. 20 (1985) 123-126 | MR 790910 | Zbl 0559.08002

[22] J. Slominski, The theory of abstract algebras with infinitary operations, Rozprawy Mat. 18 (1959) | MR 108457 | Zbl 0178.34104