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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.11451 |
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| _version_ | 1866909465812402176 |
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| author | Abraham, Uri Bonnet, Robert Džamonja, Mirna Pouzet, Maurice |
| author_facet | Abraham, Uri Bonnet, Robert Džamonja, Mirna Pouzet, Maurice |
| contents | The following is a 2008 conjecture of Abraham, Bonnet and Kubiś: [ABK Conjecture] Every well quasi order (wqo) is a countable union of better quasi orders (bqo). We obtain a partial progress on the conjecture, by showing that the class of orders that are a countable union of better quasi orders (sigma-bqo) is closed under various operations. These include diverse products, such as the Dress-Shieffels product. We develop various properties of the latter product. In relation with the main question, we explore the class of alpha-wqo for countable ordinals alpha and obtain several closure properties and a Hausdorff-style classification theorem. Our main contribution is the discovery of various properties of sigma-bqos and ruling out potential counterexamples to the ABK Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11451 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the ABK Conjecture, alpha-well Quasi Orders and Dress-Schiffels product Abraham, Uri Bonnet, Robert Džamonja, Mirna Pouzet, Maurice Logic Logic in Computer Science The following is a 2008 conjecture of Abraham, Bonnet and Kubiś: [ABK Conjecture] Every well quasi order (wqo) is a countable union of better quasi orders (bqo). We obtain a partial progress on the conjecture, by showing that the class of orders that are a countable union of better quasi orders (sigma-bqo) is closed under various operations. These include diverse products, such as the Dress-Shieffels product. We develop various properties of the latter product. In relation with the main question, we explore the class of alpha-wqo for countable ordinals alpha and obtain several closure properties and a Hausdorff-style classification theorem. Our main contribution is the discovery of various properties of sigma-bqos and ruling out potential counterexamples to the ABK Conjecture. |
| title | On the ABK Conjecture, alpha-well Quasi Orders and Dress-Schiffels product |
| topic | Logic Logic in Computer Science |
| url | https://arxiv.org/abs/2303.11451 |