| An extension of Harrington's noncupping theorem |
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| 作者姓名： | 喻良 丁德成 |
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| 作者单位： | Department of Mathematics,Nanjing University,Nanjing 210093,China,Department of Mathematics,Nanjing University,Nanjing 210093,China |
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| 摘 要： | (i) Call a c.e. degree b anti-cupping relative to x, if there is a c.e. a < b such that for any c.e. w, w x implies a ∪ w b ∪ x.(ii) Call a c.e. degree b everywhere anti-cupping (e.a.c.), if it is anti-cupping relative to x for each c.e. degree x.By a tree method, we prove that every high c.e. degree has e.a.c. property by extending Harrington's anti-cupping theorem.
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An extension of Harrington’s noncupping theorem |
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| Yu?Liang,Ding?Decheng?Email author.An extension of Harrington's noncupping theorem[J].Science in China(Information Sciences),2003,46(3):199-209. |
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| Authors: | Yu?Liang Email author" target="_blank">Ding?Decheng?Email author |
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| Affiliation: | Department of Mathematics, Nanjing Univeristy, Nanjing 210093, China |
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| Abstract: | (i) Call a c.e. degree b anti-cupping relative to x, if there is a c.e. a ＜ b such that foranyc.e. w w ximpliesaUw bUx.(ii) Call a c.e. degree b everywhere anti-cupping (e.a.c.), if it is anti-cupping relative to x foreach c.e. degree x.By a tree method, we prove that every high c.e. degree has e.a.c. property by extendingHarrington's anti-cupping theorem. |
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| Keywords: | anti-cupping property noncuppable high T-degrees computably enumerable set |
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