|ISSN 1088-6826(online) ISSN 0002-9939(print)|
Reduction of systems of linear equations in ordinal variables
Abstract: In this note we are concerned with a general finite system
of m linear equations in n variables, where the and the are positive ordinals, and the variables range over ordinals.
In the particular case n = 1 we show that (S) can be reduced to a canonical form having solutions of a relatively simple type, and we use to obtain the solution-set of (S).
In the general case we show that (S) can be reduced to a finite sequence of single-variable systems, and again obtain the solution-set of (S) in terms of the solution-sets of these simpler systems.
We assume a knowledge of the elementary theory of ordinal arithmetic, such as may be found for example in .
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