| 超实数域R的基数 |
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| 引用本文： | 冯汉桥. 超实数域R的基数[J]. 陕西师范大学学报(自然科学版), 1990, 0(1) |
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| 作者姓名： | 冯汉桥 |
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| 作者单位： | 陕西师大计算机科学系 |
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| 摘 要： | 本文证明了在 k-饱和的分析的非标准模型中,~*N,~*Q,~*R,~*N-N,~*Q-Q,~*R-R,~*R 的每个非有限的~*-有限子集,每个单子,每个银河,~*R 的所有单子之集,所有银河之集,~*R 的稠密子集,~*R 中的所有空隙之集的基数均不小于 k;~*R 的Q-拓扑,S-拓扑的基数不小于2~k.
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| 关 键 词： | 分析的非标准模型 k-饱和性 超实数域 内集 |
Cardinalities of Hyperreal Number Fields |
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| Feng Hanqiao. Cardinalities of Hyperreal Number Fields[J]. Journal of Shaanxi Normal University: Nat Sci Ed, 1990, 0(1) |
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| Authors: | Feng Hanqiao |
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| Affiliation: | Department of Computer Science |
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| Abstract: | It is shown that in a k-saturated nonstandard model of analysis,each of the following sets has cardinality at least k:~*N,~*Q,~*R,~*N-N,~*Q-Q,~*R-R, a non-finite ~*finite subset of ~*R,a monad of ~*R,a galaxy of ~*R,a dense su- bset of ~*R,the set of monads of ~*R,the set of galaxies of ~*R,the set of gaps in ~*R,the set of gaps in a monad of ~*R,and that each of the Q-topology and S-topology for ~*R has eardinality at least 2~k. |
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| Keywords: | nonstandard model of analysis k-saturation hyperreal numer field internal set |
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