发表机构
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Vaught猜想的一个新变体，基于Martin猜想和$\omega$-Vaught猜想，针对$\omega$-稳定理论证明之，并将Scott句所需量词数从$\omega+\omega$改进为$\omega+5$（可数情形）和$\omega+6$（不可数情形）。
AI 中文摘要
我们基于Martin（模型论）猜想以及Gonzalez和Montalbán的$\omega$-Vaught猜想，提出了Vaught猜想的一个新变体。对于$\omega$-稳定理论，我们通过详细分析Bouscaren以及Shelah-Harrington-Makkai分别对Martin猜想和Vaught猜想的证明来证明该猜想。特别地，当存在可数个可数模型时，我们将Scott句所需的量词数量从$\omega+\omega$改进为$\omega+5$，并在不可数情形下获得类似的界$\omega+6$。
英文摘要
We propose a new variant of Vaught's conjecture, based on Martin's (model-theoretic) conjecture and the $ω$-Vaught's conjecture of Gonzalez and Montalbán. For $ω$-stable theories, we prove the conjecture by analyzing in detail Bouscaren's and Shelah-Harrington-Makkai's proofs of Martin's conjecture and Vaught's conjecture, respectively, for $ω$-stable theories. In particular, when there are countably many countable models, we improve the required number of quantifiers for a Scott sentence from $ω+ω$ to $ω+5$, and we obtain a similar bound of $ω+6$ for the uncountable case.
Comments15 pages
