Hyperhypersimple sets and \(\Delta _ 2\) systems (Q1823933)
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scientific article; zbMATH DE number 4116520
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hyperhypersimple sets and \(\Delta _ 2\) systems |
scientific article; zbMATH DE number 4116520 |
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Hyperhypersimple sets and \(\Delta _ 2\) systems (English)
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1989
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A reverse-mathematics approach to hyperhypersimple sets - starting from the axioms of Peano arithmetic with the induction schema omitted, how much axiomatic strength need be added to obtain basic results on hyperhypersimplicity? The author shows that \(\Sigma_ 2\) induction is sufficient, but not necessary, to ensure the equivalence of (Yates' simplification of) Post's original definition of hyperhypersimplicity with Lachlan's lattice-theoretic characterization. The paper's main result, obtained using the notion of a \(\Delta_ 2\) system, is that \(\Sigma_ 2\) collection suffices to prove the existence of hyperhypersimple sets.
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reverse mathematics
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hyperhypersimple sets
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\(\Sigma _ 2\) induction
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\(\Delta _ 2\) system
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\(\Sigma _ 2\) collection
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