This chapter introduces some techniques for constructing elementary simple extensions. In particular, it includes proof of the existence of superminimal elementary end extensions of countable models and a construction of a Jónsson model. The MacDowell-Specker Theorem is proved and some of its consequences derived, including results on conservative extensions, rather classless models and amalgamations. The chapter concludes with a discussion of nonelementary extensions and the theorem of Wilkie on end extensions which are not σ1-elementary.
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