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A categorical construction of Bachmann–Howard fixed points

Freund, Anton (2024)
A categorical construction of Bachmann–Howard fixed points.
In: Bulletin of the London Mathematical Society, 2019, 51 (5)
doi: 10.26083/tuprints-00016166
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: A categorical construction of Bachmann–Howard fixed points
Language: English
Date: 26 January 2024
Place of Publication: Darmstadt
Year of primary publication: 2019
Place of primary publication: Hoboken
Publisher: Wiley
Journal or Publication Title: Bulletin of the London Mathematical Society
Volume of the journal: 51
Issue Number: 5
DOI: 10.26083/tuprints-00016166
Corresponding Links:
Origin: Secondary publication DeepGreen

Peter Aczel has given a categorical construction for fixed points of normal functors, that is, dilators which preserve initial segments. For a general dilator X↦TX, we cannot expect to obtain a well‐founded fixed point, as the order type of TX may always exceed the order type of X. In the present paper, we show how to construct a Bachmann–Howard fixed point of T, that is, an order BH(T) with an ‘almost’ order preserving collapse ϑ:TBH(T)→BH(T). Building on previous work, we show that Π11‐comprehension is equivalent to the assertion that BH(T) is well‐founded for any dilator T.

Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-161663
Additional Information:

Mathematics Subject Classification: 03B30, 03D60, 03F15 (primary)

Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Logic
Date Deposited: 26 Jan 2024 13:48
Last Modified: 27 Feb 2024 13:52
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/16166
PPN: 515845612
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