well-ordering


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well-ordering

n
(Logic) logic maths an ordering in which every nonempty subset has a least member under the relation
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For this purpose, a well-ordering of the real closed field is assumed to be given.
Now [DKKL] shows that the construction of IPs for countable RCFs is constructible given a residue field section and a well-ordering of K.
(ZF) Let K be a real closed field and [??] a well-ordering of K.
Among the topics are the Ershov hierarchy, definability in the real universe, experiments on an internal approach to typed algorithms in analysis, and reverse mathematics and well-ordering principles.
Ideas from Husserl's phenomenology are used in the second half to obtain precise characterization of what is and is not evident about choice and thereby to distinguish it in terms of evidential style from the formally equivalent well-ordering principle--a distinction that is crucial for Zermelo's proof of the well-ordering theorem.
When the Pilgrims landed at Plymouth in 1620, among the first things they did for the well-ordering of their new commonwealth was to institute the Dutch custom of civil marriage with which they had become familiar during their long sojourn in the Netherlands.
Similarly, there is an IF first-order sentence that says that a relation R is not a well-ordering, and an extended IF first-order sentence that says that R is a well-ordering.