Geodesic
Cardinal and ordinal arithmetics of $n$-ary relational systems and $n$-ary ordered sets
Mathematica Bohemica, Tome 123 (1998) no. 3, pp. 249-262.

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The aim of this paper is to define and study cardinal (direct) and ordinal operations of addition, multiplication, and exponentiation for $n$-ary relational systems. $n$-ary ordered sets are defined as special $n$-ary relational systems by means of properties that seem to suitably generalize reflexivity, antisymmetry, and transitivity from the case of $n=2$ or 3. The class of $n$-ary ordered sets is then closed under the cardinal and ordinal operations.
DOI : 10.21136/MB.1998.126071
Classification : 03E05, 03E10, 04A05, 06A99, 08A02
Keywords: cardinal sum; cardinal product; ordinal sum; ordinal product; $n$-ary relational system; $n$-ary ordered set; cardinal power; ordinal power 
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Karásek, Jiří. Cardinal and ordinal arithmetics of $n$-ary relational systems and $n$-ary ordered sets. Mathematica Bohemica, Tome 123 (1998) no. 3, pp. 249-262. doi : 10.21136/MB.1998.126071. http://geodesic.mathdoc.fr/articles/10.21136/MB.1998.126071/

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