Freund, Anton (2020)
What is effective transfinite recursion in reverse mathematics?
In: Mathematical Logic Quarterly, 66 (4)
doi: 10.1002/malq.202000042
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
In the context of reverse mathematics, effective transfinite recursion refers to a principle that allows us to construct sequences of sets by recursion along arbitrary well orders, provided that each set is Δ¹₀‐definable relative to the previous stages of the recursion. It is known that this principle is provable in ACA₀. In the present note, we argue that a common formulation of effective transfinite recursion is too restrictive. We then propose a more liberal formulation, which appears very natural and is still provable in ACA₀.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2020 |
| Autor(en): | Freund, Anton |
| Art des Eintrags: | Bibliographie |
| Titel: | What is effective transfinite recursion in reverse mathematics? |
| Sprache: | Englisch |
| Publikationsjahr: | 2020 |
| Ort: | Weinheim |
| Verlag: | Wiley-VCH |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Mathematical Logic Quarterly |
| Jahrgang/Volume einer Zeitschrift: | 66 |
| (Heft-)Nummer: | 4 |
| DOI: | 10.1002/malq.202000042 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | In the context of reverse mathematics, effective transfinite recursion refers to a principle that allows us to construct sequences of sets by recursion along arbitrary well orders, provided that each set is Δ¹₀‐definable relative to the previous stages of the recursion. It is known that this principle is provable in ACA₀. In the present note, we argue that a common formulation of effective transfinite recursion is too restrictive. We then propose a more liberal formulation, which appears very natural and is still provable in ACA₀. |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Logik |
| Hinterlegungsdatum: | 12 Mär 2024 09:46 |
| Letzte Änderung: | 12 Mär 2024 09:46 |
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| Suche nach Titel in: | TUfind oder in Google |
Verfügbare Versionen dieses Eintrags
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What is effective transfinite recursion in reverse mathematics? (deposited 30 Jan 2024 13:56)
- What is effective transfinite recursion in reverse mathematics? (deposited 12 Mär 2024 09:46) [Gegenwärtig angezeigt]
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