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 |
| Abstract: | 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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