Unstable First-order Theories
نویسنده
چکیده
In this paper, we examine the divide between stable and unstable first-order theories in model theory. We begin by defining a stable theory and proving Shelah’s theorem, which reduces the question of stability to a problem of examining a single formula. Afterwards, we will provide some applications of the stability/instability divide to other model-theoretic questions, such as the question of categoricity in power or the existence of saturated models. Along the way, we will explore other model-theoretic topics pertinent to the questions at hand, and examine numerous examples to keep our bearing.
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