On Decidable Fragments of Theories in Field Arithmetic
碩士 === 國立交通大學 === 應用數學系所 === 106 === In this thesis, we prove the preservation theorem of ∀^n∃ sentences over number fields under existentially closedness. We show that the ∃∀ theories of Hilbertian fields with characteristic 0 and perfect Hilbertian fields are both decidable. We also prove that th...
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| Format: | Others |
| Language: | en_US |
| Published: |
2018
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| Online Access: | http://ndltd.ncl.edu.tw/handle/pp7377 |
| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 106 === In this thesis, we prove the preservation theorem of ∀^n∃ sentences over number fields under existentially closedness. We show that the ∃∀ theories of Hilbertian
fields with characteristic 0 and perfect Hilbertian fields are both decidable. We also prove that the ∀∃ theories of Hilbertian fields with characteristic 0, Hilbertian fields,
PAC fields with characteristic 0, and PAC fields are all decidable.
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