Freund, Anton (2024)
What is effective transfinite recursion in reverse mathematics?
In: Mathematical Logic Quarterly, 2020, 66 (4)
doi: 10.26083/tuprints-00017787
Article, Secondary publication, Publisher's Version
 | There is a more recent version of this item available. |
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2024 |
| Creators: | Freund, Anton |
| Type of entry: | Secondary publication |
| Title: | What is effective transfinite recursion in reverse mathematics? |
| Language: | English |
| Date: | 30 January 2024 |
| Place of Publication: | Darmstadt |
| Year of primary publication: | 2020 |
| Place of primary publication: | Weinheim |
| Publisher: | Wiley-VCH |
| Journal or Publication Title: | Mathematical Logic Quarterly |
| Volume of the journal: | 66 |
| Issue Number: | 4 |
| DOI: | 10.26083/tuprints-00017787 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/17787 |
| Corresponding Links: | |
| Origin: | Secondary publication DeepGreen |
| 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. |
| Status: | Publisher's Version |
| URN: | urn:nbn:de:tuda-tuprints-177872 |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics |
| Divisions: | 04 Department of Mathematics 04 Department of Mathematics > Logic |
| Date Deposited: | 30 Jan 2024 13:56 |
| Last Modified: | 12 Mar 2024 09:46 |
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| Suche nach Titel in: | TUfind oder in Google |
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