| The Theory of Finite Models without Equal Sign |
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| 作者姓名： | Li Bo LUO |
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| 作者单位： | [1]Department of Mathematics Science, Guizhou College for Minorities, Guiyang 550025, P. R. China [2]Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China |
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| 基金项目： | This project is supported by the research foundation of Guangdong Women＇s Professional Technical College |
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| 摘 要： | In this paper, it is the first time ever to suggest that we study the model theory of all finite structures and to put the equal sign in the same situtation as the other relations. Using formulas of infinite lengths we obtain new theorems for the preservation of model extensions, submodels, model homomorphisms and inverse homomorphisms. These kinds of theorems were discussed in Chang and Keisler＇s Model Theory, systematically for general models, but Gurevich obtained some different theorems in this direction for finite models. In our paper the old theorems manage to survive in the finite model theory. There are some differences between into homomorphisms and onto homomorphisms in preservation theorems too. We also study reduced models and minimum models. The characterization sentence of a model is given, which derives a general result for any theory T to be equivalent to a set of existential-universal sentences. Some results about completeness and model completeness are also given.
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| 关 键 词： | 有限模型 等号 保存定理 模型扩展 |
| 收稿时间： | 2003-05-21 |
| 修稿时间： | 2003-05-212004-09-14 |
The Theory of Finite Models without Equal Sign |
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| Li Bo LUO.The Theory of Finite Models without Equal Sign[J].Acta Mathematica Sinica,2006,22(3):865-872. |
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| Authors: | Li Bo Luo |
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| Institution: | (1) Department of Mathematics Science, Guizhou College for Minorities, Guiyang 550025, P. R. China;(2) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China |
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| Abstract: | In this paper, it is the first time ever to suggest that we study the model theory of all finite structures and to put the
equal sign in the same situtation as the other relations. Using formulas of infinite lengths we obtain new theorems for the
preservation of model extensions, submodels, model homomorphisms and inverse homomorphisms. These kinds of theorems were discussed
in Chang and Keisler's Model Theory, systematically for general models, but Gurevich obtained some different theorems in this
direction for finite models. In our paper the old theorems manage to survive in the finite model theory. There are some differences
between into homomorphisms and onto homomorphisms in preservation theorems too. We also study reduced models and minimum models.
The characterization sentence of a model is given, which derives a general result for any theory T to be equivalent to a set of existential–universal sentences. Some results about completeness and model completeness are
also given.
This project is supported by the research foundation of Guangdong Women's Professional Technical College |
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| Keywords: | Finite models Equal sign Preservation theorems |
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