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Keywords:
monounary algebra; homogeneous; 2-homogeneous; 2-set-homogeneous
monounary algebra; homogeneous; 2-homogeneous; 2-set-homogeneous
Summary:
Fraïssé introduced the notion of a $k$-set-homogeneous relational structure. In the present paper the following classes of monounary algebras are described: $\mathcal Sh_2(S)$, $\mathcal Sh_2(S^c)$, $\mathcal Sh_2(P^c)$ —the class of all algebras which are 2-set-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively, and $\mathcal H_2(S)$, $\mathcal H_2(S^c)$, $\mathcal H_2(P^c)$ —the class of all algebras which are 2-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively.
References:
[1] B. Csákány: Homogeneous algebras. In: Contributions to General Algebra. Proc. Klagenfurt Conference, 1978, Verlag J. Heyn, Klagenfurt, 1979, pp. 77–81. MR 0537408
[2] B. Csákány: Homogeneous algebras are functionally complete. Algebra Universalis 11 (1980), 149–158. DOI 10.1007/BF02483093 | MR 0588208
[3] B. Csákány and T. Gavalcová: Finite homogeneous algebras I. Acta Sci. Math. 42 (1980), 57–65. MR 0576935
[4] M. Droste and H. D. Macpherson: On $k$-homogeneous posets and graphs. J. Comb. Theory Ser. A 56 (1991), 1–15. DOI 10.1016/0097-3165(91)90018-C | MR 1082839
[5] M. Droste, M. Giraudet, H. D. Macpherson and N. Sauer: Set-homogeneous graphs. J. Comb. Theory Ser. B 62 (1994), 63–95. DOI 10.1006/jctb.1994.1055 | MR 1290631
[6] M. Droste, M. Giraudet and D. Macpherson: Set-homogeneous graphs and embeddings of total orders. Order 14 (1997), 9–20. DOI 10.1023/A:1005880810385 | MR 1468952
[7] R. Fraïssé: Theory of Relations. North-Holland, Amsterdam, 1986. MR 0832435
[8] B. Ganter, J. Płonka and H. Werner: Homogeneous algebras are simple. Fund. Math. 79 (1973), 217–220. DOI 10.4064/fm-79-3-217-220 | MR 0319859
[9] D. Jakubíková-Studenovská: Homogeneous monounary algebras. Czechoslovak Math. J. 52 (2002), 309–317. DOI 10.1023/A:1021722527256 | MR 1905437
[10] D. Jakubíková-Studenovská: On homogeneous and 1-homogeneous monounary algebras. In: Contributions to General Algebra 12. Proceedings of the Vienna Conference, June, 1999, Verlag J. Heyn, Klagenfurt, 2000, pp. 222–224.
[11] E. Marczewski: Homogeneous algebras and homogeneous operations. Fund. Math. 56 (1964), 81–103. DOI 10.4064/fm-56-1-81-103 | MR 0176950
[12] A. H. Mekler: Homogeneous partially ordered sets. In: Finite and Infinite Combinatorics in Sets and Logic. Proceeding NATO ASI conference in Banf 1991, N. W. Sauer, R. E. Woodrow and B. Sands (eds.), Kluwer, Dordrecht, 1993, pp. 279–288. MR 1261211 | Zbl 0845.06002
[13] R. S. Pierce: Some questions about complete Boolean algebras. In: Lattice Theory, Proc. Symp. Pure Math, Vol. II, AMS, Providence, 1961, pp. 129–140. MR 0138570 | Zbl 0101.27104
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