Cardinal and ordinal arithmetics of -ary relational systems and -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
top- G. Birkhoff, 10.1215/S0012-7094-37-00323-5, Duke Math. J. 3 (1937), 311-316. (1937) Zbl0016.38702MR1545989DOI10.1215/S0012-7094-37-00323-5
- G. Birkhoff, 10.1215/S0012-7094-42-00921-9, Duke Math. J. V (1942), 283-302. (1942) Zbl0060.12609MR0007031DOI10.1215/S0012-7094-42-00921-9
- G. Birkhoff, Lattice Theory, Amer. Math. Soc., Providence, Rhode Island, Third Edition, 1973. (1973) MR0227053
- M. M. Day, 10.1090/S0002-9947-1945-0012262-4, Trans. Amer. Math. Soc. 58 (1945), 1-43. (1945) Zbl0060.05813MR0012262DOI10.1090/S0002-9947-1945-0012262-4
- V. Novák, On a power of relational structures, Czechoslovak Math. J. 35 (1985), 167-172. (1985) MR0779345
- V. Novák M. Novotný, Binary and ternary relations, Math. Bohem. 117(1992), 283-292. (1992) MR1184541
- V. Novák M. Novotný, Pseudodimension of relational structures, Czechoslovak Math. J. (submitted). MR1708362
- J. Šlapal, Direct arithmetics of relational systems, Publ. Math. Debrecen 38 (1991), 39-48. (1991) MR1100904
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