Abstract
We discuss minimal elementary extensions of models of set theory and contrast the behavior of models of set theory and arithmetic as regarding such extensions. Our main result, proved using a Boolean ultrapower argument, is:
Theorem
Every model of ZFChas a conservative elementary extension which possesses a cofinal minimal elementary extension.An application of Boolean ultrapowers to models of full arithmetic is also presented.
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Enayat, A. Minimal elementary extensions of models of set theory and arithmetic. Arch Math Logic 30, 181–192 (1990). https://doi.org/10.1007/BF01621470
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DOI: https://doi.org/10.1007/BF01621470