A Course on Basic Model Theory by Haimanti Sarbadhikari & Shashi Mohan Srivastava

Author:Haimanti Sarbadhikari & Shashi Mohan Srivastava
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

Hence, .

Consider the map defined by . By Lemma 3.​3.​4, . By induction hypothesis, . It follows that .

Example 4.8.2

Consider DLO. In Example 3.​4.​17 we saw that . Hence, DLO is not -stable.

Example 4.8.3

Now consider RCF and RCOF and with usual interpretations. In Example 3.​4.​15, we showed that viewing as a model of RCOF, . Hence, RCOF is not -stable. Since < is definable in the field , it follows that RCF is not -stable.

Example 4.8.4

Let , and the subfield generated by A. Then . In Example 3.​4.​18 we observed that

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