Upper Bound Principle

Some articles on upper bound principle, upper bound, principle:

Constructive Analysis - Examples - The Least Upper Bound Principle and Compact Sets
... is that constructive analysis does not accept the least upper bound principle, that any subset of the real line R has a least upper bound (or supremum ... exists an element s of S such that x < s, or y is an upper bound of S.) Again, this is classically equivalent to the full least upper bound principle, since every set is located in ...
Specker Sequence
... exist means that the collection of all computable real numbers does not satisfy the least upper bound principle of real analysis, even when considering only computable sequences ... The least upper bound principle has also been analyzed in the program of reverse mathematics, where the exact strength of this principle has been determined ... In the terminology of that program, the least upper bound principle is equivalent to ACA0 over RCA0 ...

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