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What is effective transfinite recursion in reverse mathematics?

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

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Item Type: Article
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
Corresponding Links:
Origin: Secondary publication DeepGreen

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 > Logic
Date Deposited: 30 Jan 2024 13:56
Last Modified: 01 Feb 2024 14:37
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/17787
PPN: 515148156
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