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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MR Zbl
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.
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 
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
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