Untranscendable order types
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914358013984768 |
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| author | Ervin, Garrett Marcone, Alberto Weinert, Thilo |
| author_facet | Ervin, Garrett Marcone, Alberto Weinert, Thilo |
| contents | We introduce and study a multiplicative analogue of additive indecomposability for linear order types that we call untranscendability, as well as a strengthening that we call $s$-untranscendability. We show that, with the unique exception of the two-point type, every untranscendable type is additively indecomposable, and every $σ$-scattered untranscendable type is strongly indecomposable. Under the Proper Forcing Axiom, every untranscendable Aronszajn type is strongly indecomposable. We also show that a theorem of Hagendorf and Jullien, that every strictly additively indecomposable type must be strictly indecomposable to either the left or right, has a natural analogue for $s$-untranscendable types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_24285 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Untranscendable order types Ervin, Garrett Marcone, Alberto Weinert, Thilo Combinatorics Logic 06A05 (Primary), 03E25, 03E57, 03E60 (Secondary) We introduce and study a multiplicative analogue of additive indecomposability for linear order types that we call untranscendability, as well as a strengthening that we call $s$-untranscendability. We show that, with the unique exception of the two-point type, every untranscendable type is additively indecomposable, and every $σ$-scattered untranscendable type is strongly indecomposable. Under the Proper Forcing Axiom, every untranscendable Aronszajn type is strongly indecomposable. We also show that a theorem of Hagendorf and Jullien, that every strictly additively indecomposable type must be strictly indecomposable to either the left or right, has a natural analogue for $s$-untranscendable types. |
| title | Untranscendable order types |
| topic | Combinatorics Logic 06A05 (Primary), 03E25, 03E57, 03E60 (Secondary) |
| url | https://arxiv.org/abs/2602.24285 |