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cardinal sum; cardinal product; ordinal sum; ordinal product; $n$-ary relational system; $n$-ary ordered set; cardinal power; ordinal power

References:

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[2] G. Birkhoff: **Generalized arithmetic**. Duke Math. J. V (1942), 283-302. DOI 10.1215/S0012-7094-42-00921-9 | MR 0007031 | Zbl 0060.12609

[3] G. Birkhoff: **Lattice Theory**. Amer. Math. Soc., Providence, Rhode Island, Third Edition, 1973. MR 0227053

[4] M. M. Day: **Arithmetic of ordered systems**. Trans. Amer. Math. Soc. 58 (1945), 1-43. DOI 10.1090/S0002-9947-1945-0012262-4 | MR 0012262 | Zbl 0060.05813

[5] V. Novák: **On a power of relational structures**. Czechoslovak Math. J. 35 (1985), 167-172. MR 0779345

[6] V. Novák M. Novotný: **Binary and ternary relations**. Math. Bohem. 117(1992), 283-292. MR 1184541

[7] V. Novák M. Novotný: **Pseudodimension of relational structures**. Czechoslovak Math. J. (submitted). MR 1708362

[8] J. Šlapal: **Direct arithmetics of relational systems**. Publ. Math. Debrecen 38 (1991), 39-48. MR 1100904