منابع مشابه
A Dividing Line within Simple Unstable Theories
We give the first (ZFC) dividing line in Keisler’s order among the unstable theories, specifically among the simple unstable theories. That is, for any infinite cardinal λ for which there is μ < λ ≤ 2, we construct a regular ultrafilter D on λ such that (i) for any model M of a stable theory or of the random graph, M/D is λ-saturated but (ii) if Th(N) is not simple or not low then N/D is not λ-...
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We prove a consistency results saying, that for a simple (first order) theory, it is easier to have a universal model in some cardinalities, than for the theory of linear order. We define additional properties of first order theories, the n-strong order property (SOPn in short). The main result is that a first order theory with the 4-strong order property behaves like linear orders concerning e...
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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 c...
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The aim of this paper is to define various properties of formulas in first order theories, and prove the appropriate implications between these properties. Most definitions are taken from [3], but the definitions themselves and many of the proofs are due to Shelah (see [4, II]). We give citations at the beginning of proofs taken from other sources. Recall that a theory is stable if no formula h...
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We prove a consistency results saying, that for a simple (first order) theory, it is easier to have a universal model in some cardinalities, than for the theory of linear order. We define additional properties of first order theories, the n-strong order property (SOPn in short). The main result is that a first order theory with the 4-strong order property behaves like linear orders concerning e...
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ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1980
ISSN: 0003-4843
DOI: 10.1016/0003-4843(80)90009-1