For a class of finite graphs, we define a limit object relative to some computationally restricted class of functions. The properties of the limit object then reflect how a computationally restricted viewer "sees" a generic instance from the class. The construction uses Kraj\'i\v{c}ek's forcing with random variables [7]. We prove sufficient conditions for universal and existential sentences to be valid in the limit, provide several examples, and prove that such a limit object can then be expanded to a model of weak arithmetic. We then take the limit of all finite pointed paths to obtain a model of arithmetic where the problem OntoWeakPigeon is total but Leaf (the complete problem for $\textbf{PPA}$) is not. This can be viewed as a logical separation of the oracle classes of total NP search problems, which in our setting implies standard nonreducibility of Leaf to OntoWeakPigeon.

翻译：对于一类有限图，我们定义了相对于某计算受限函数类的极限对象。该极限对象的性质反映了计算受限的观察者如何"看待"该类中的一般实例。该构造使用了Krajíček的随机变量力迫法[7]。我们证明了极限中全称句与存在句成立的有效充分条件，给出了若干示例，并证明了该极限对象可扩展为弱算术模型。随后，通过对所有有限有根路径取极限，我们得到了一个算术模型，在该模型中OntoWeakPigeon问题是完全的，而Leaf（$\textbf{PPA}$的完全问题）则不是。这可视为对完全NP搜索问题预言类的一种逻辑分离，在我们的设定下意味着Leaf无法归约到OntoWeakPigeon的标准不可归约性。