Limit models in strictly stable abstract elementary classes

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2024-12-02 DOI:10.1002/malq.202200075

Will Boney, Monica M. VanDieren

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Abstract

In this paper, we examine the locality condition for non-splitting and determine the level of uniqueness of limit models that can be recovered in some stable, but not superstable, abstract elementary classes. In particular we prove the following. Suppose that $K$ is an abstract elementary class satisfying

Then for $ϑ$ and $δ$ limit ordinals $< μ^{+}$ both with cofinality $\geq κ_{μ}^{*} (K)$ , if $K$ satisfies symmetry for $non - μ - splitting$ (or just $(μ, δ)$ -symmetry), then, for any $M_{1}$ and $M_{2}$ that are $(μ, ϑ)$ and $(μ, δ)$ -limit models over $M_{0}$ , respectively, we have that $M_{1}$ and $M_{2}$ are isomorphic over $M_{0}$ . Note that no tameness is assumed.

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严格稳定抽象初等类的极限模型

本文研究了非分裂的局部性条件，并确定了在稳定但非超稳定的抽象初等类中可以恢复的极限模型的唯一性水平。我们特别证明了以下几点。假设K $\mathcal {K}$ 一个抽象的初等类是否满足Then $\vartheta$ δ $\delta$ 极限序数＆lt；μ + $<\mu ^+$ 均具有合度≥κ μ∗(K) $\ge \kappa ^*_\mu (\mathcal {K})$ ，如果K $\mathcal {K}$ 满足非μ分裂的对称性 ${\rm non}\text{-}\mu\text{-}{\rm splitting}$ (或只是（μ, δ） $(\mu,\delta)$ -对称)，然后，对于任何m1 $M_1$ 和m2 $M_2$ 即（μ,） $(\mu,\vartheta)$ 和（μ, δ） $(\mu,\delta)$ - m0以上的极限模型 $M_0$ 分别得到m1 $M_1$ 和m2 $M_2$ 在m0上是同构的 $M_0$ ．注意，这里没有假设驯服性。

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.