| Summary: | 碩士 === 國立中正大學 === 哲學研究所 === 102 === The main work of this thesis research is divided into three parts:
1. I restate Euclidean geometry postulate system in first–order logic language. To accomplish this work, I sort out the information including Hilbert's axioms, geometry definitions, and theorems in the first chapter, and I introduce the basic concepts of logic and model theory in chapter 2.
2. Relying on the establishment of different models, we can illustrate the compatibility and the independence between these axioms. Most of these models are constructed in Euclidean geometry, and the construction process of these models is interesting. But some models require more mathematical knowledge to realize their meaning.
3. According to the establishment of non–Euclidean geometry models in Euclidean space, we can show that the consistency of Euclidean geometry implies the consistency of non–Euclidean geometry.
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