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A Logarithmic Property for Exponents of Partially Ordered Sets

Published online by Cambridge University Press:  20 November 2018

Dwight Duffus  and
Ivan Rival
Dwight Duffus
Affiliation:
The University of Calgary Calgary, Alberta
Ivan Rival
Affiliation:
The University of Calgary Calgary, Alberta
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In an effort to unify the arithmetic of cardinal and ordinal numbers, Garrett Birkhoff [2; 3; 4; 5] (cf. [6]) defined several operations on partially ordered sets of which at least one, (cardinal) exponentiation, is of considerable independent interest: for partially ordered sets P and Q let PQ denote the set of all order-preserving maps of Q to P partially ordered by f ≦ g if and only if f(x) ≦ g(x) for each x ∈ Q.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 4 , 01 August 1978 , pp. 797 - 807
Copyright
Copyright © Canadian Mathematical Society 1978

References

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