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A five element basis for the uncountable linear orders
In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) that the class of uncountable linear orders has a five element basis. In fact such a basis follows fro...
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| Lenguaje: | eng |
| Publicado: |
2005
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| Acceso en línea: | http://cds.cern.ch/record/853825 |
| _version_ | 1780907024915103744 |
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| author | Moore, J T |
| author_facet | Moore, J T |
| author_sort | Moore, J T |
| collection | CERN |
| description | In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) that the class of uncountable linear orders has a five element basis. In fact such a basis follows from the Proper Forcing Axiom, a strong form of the Baire Category Theorem. The elements are X, omega_1, omega_1^*, C, C^* where X is any suborder of the reals of cardinality aleph_1 and C is any Countryman line. This confirms a longstanding conjecture of Shelah. |
| id | cern-853825 |
| institution | Organización Europea para la Investigación Nuclear |
| language | eng |
| publishDate | 2005 |
| record_format | invenio |
| spelling | cern-8538252019-09-30T06:29:59Zhttp://cds.cern.ch/record/853825engMoore, J TA five element basis for the uncountable linear ordersMathematical Physics and MathematicsIn this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) that the class of uncountable linear orders has a five element basis. In fact such a basis follows from the Proper Forcing Axiom, a strong form of the Baire Category Theorem. The elements are X, omega_1, omega_1^*, C, C^* where X is any suborder of the reals of cardinality aleph_1 and C is any Countryman line. This confirms a longstanding conjecture of Shelah.math.LO/0501525oai:cds.cern.ch:8538252005-01-28 |
| spellingShingle | Mathematical Physics and Mathematics Moore, J T A five element basis for the uncountable linear orders |
| title | A five element basis for the uncountable linear orders |
| title_full | A five element basis for the uncountable linear orders |
| title_fullStr | A five element basis for the uncountable linear orders |
| title_full_unstemmed | A five element basis for the uncountable linear orders |
| title_short | A five element basis for the uncountable linear orders |
| title_sort | five element basis for the uncountable linear orders |
| topic | Mathematical Physics and Mathematics |
| url | http://cds.cern.ch/record/853825 |
| work_keys_str_mv | AT moorejt afiveelementbasisfortheuncountablelinearorders AT moorejt fiveelementbasisfortheuncountablelinearorders |