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- Q2308311 subject Q8407451.
- Q2308311 abstract "In computability theory, a Specker sequence is a computable, monotonically increasing, bounded sequence of rational numbers whose supremum is not a computable real number. The first example of such a sequence was constructed by Ernst Specker in 1949. The existence of Specker sequences has consequences for computable analysis. The fact that such sequences 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. A common way to resolve this difficulty is to consider only sequences that are accompanied by a modulus of convergence; no Specker sequence has a computable modulus of convergence. 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.".
- Q2308311 thumbnail SuiteSpecker.svg?width=300.
- Q2308311 wikiPageWikiLink Q1148456.
- Q2308311 wikiPageWikiLink Q117486.
- Q2308311 wikiPageWikiLink Q1254734.
- Q2308311 wikiPageWikiLink Q17502105.
- Q2308311 wikiPageWikiLink Q1783484.
- Q2308311 wikiPageWikiLink Q2005236.
- Q2308311 wikiPageWikiLink Q5157264.
- Q2308311 wikiPageWikiLink Q5157271.
- Q2308311 wikiPageWikiLink Q676835.
- Q2308311 wikiPageWikiLink Q818895.
- Q2308311 wikiPageWikiLink Q818930.
- Q2308311 wikiPageWikiLink Q8407451.
- Q2308311 wikiPageWikiLink Q877945.
- Q2308311 comment "In computability theory, a Specker sequence is a computable, monotonically increasing, bounded sequence of rational numbers whose supremum is not a computable real number. The first example of such a sequence was constructed by Ernst Specker in 1949. The existence of Specker sequences has consequences for computable analysis.".
- Q2308311 label "Specker sequence".
- Q2308311 depiction SuiteSpecker.svg.