We extend the concept of “almost indiscernible theory” introduced by Pillay and Sklinos in 2015 (which was itself a modernization and expansion of Baldwin and Shelah from 1983), to uncountable languages and uncountable parameter sequences. Roughly speaking a theory \(T\) is almost indiscernible if some saturated model is in the algebraic closure of an indiscernible set of sequences. We show that such a theory \(T\) is nonmultidimensional, superstable, and stable in all cardinals \(\ge |T|\). We prove a structure theorem for sufficiently large \( a \)-models \(M\), which states that over a suitable base, \(M\) is in the algebraic closure of an independent set of realizations of weight one types (in possibly infinitely many variables). We also explore further the saturated free algebras of Baldwin and Shelah in both the countable and uncountable context. We study in particular theories and varieties of \(R\)-modules, characterizing those rings \( R \) for which the free \( R \)-module on \( \left| R\right| ^{+} \) generators is saturated, and pointing out a counterexample to a conjecture by Pillay and Sklinos.

我们将 Pillay 和 Sklinos 在 2015 年引入的“几乎不可识别理论”的概念（其本身是 Baldwin 和 Shelah 从 1983 年开始的现代化和扩展）扩展到不可数的语言和不可数的参数序列。粗略地说，如果某个饱和模型处于一组不可识别序列的代数闭包中，则理论\(T\)几乎是不可识别的。我们证明了这样的理论\(T\)在所有基数\(\ge |T|\)中都是非多维的、超稳定的和稳定的。我们证明了足够大的 \( a \) -模型\(M\)的结构定理，它表明在合适的基础上，\(M\)处于代数闭包中一组独立的权重类型的实现（可能有无限多的变量）。我们还在可数和不可数上下文中进一步探索了鲍德温和谢拉的饱和自由代数。我们特别研究了\(R\) -modules的理论和变体，描述了那些环\( R \)，对于这些环 \( R \) -module 在\( \left| R\right| ^{+} \ )生成器已饱和，并指出了 Pillay 和 Sklinos 猜想的反例。