# Cardinal and ordinal arithmetics of $n$-ary relational systems and $n$-ary ordered sets

Mathematica Bohemica (1998)

- Volume: 123, Issue: 3, page 249-262
- ISSN: 0862-7959

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topKarásek, Jiří. "Cardinal and ordinal arithmetics of $n$-ary relational systems and $n$-ary ordered sets." Mathematica Bohemica 123.3 (1998): 249-262. <http://eudml.org/doc/248315>.

@article{Karásek1998,

abstract = {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.},

author = {Karásek, Jiří},

journal = {Mathematica Bohemica},

keywords = {cardinal sum; cardinal product; ordinal sum; ordinal product; $n$-ary relational system; $n$-ary ordered set; cardinal power; ordinal power; -ary relational system; -ary ordered set; cardinal sum; cardinal product; ordinal sum; ordinal product},

language = {eng},

number = {3},

pages = {249-262},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Cardinal and ordinal arithmetics of $n$-ary relational systems and $n$-ary ordered sets},

url = {http://eudml.org/doc/248315},

volume = {123},

year = {1998},

}

TY - JOUR

AU - Karásek, Jiří

TI - Cardinal and ordinal arithmetics of $n$-ary relational systems and $n$-ary ordered sets

JO - Mathematica Bohemica

PY - 1998

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 123

IS - 3

SP - 249

EP - 262

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/248315

ER -

## References

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