For an infinite class of finite graphs of unbounded size, we define a limit object, to be called wide limit, relative to some computationally restricted class of functions. The properties of the wide limit then reflect how a computationally restricted viewer "sees" a generic instance from the class. The construction uses arithmetic forcing with random variables [10]. 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 wide 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 logical separation of the oracle classes of total NP search problems in our setting implies that Leaf is not reducible to OntoWeakPigeon even if some errors are allowed in the reductions.

翻译：对于一类无界大小的有限图无限族，我们定义了一个极限对象（称为宽极限），该极限相对于某个计算受限的函数类。宽极限的性质反映了计算受限的观察者如何“看待”该类中的典型实例。该构造使用了带随机变量的算术力迫法[10]。我们证明了在极限中全称句和存在句成立的条件，给出了若干示例，并证明了此类极限对象可扩展为弱算术模型。接着，我们对所有有限有向路径取宽极限，得到一个算术模型，其中OntoWeakPigeon问题是全问题，而Leaf（$\textbf{PPA}$的完备问题）不是全问题。在我们的设定中，总NP搜索问题的谕示类之间的这一逻辑分离表明：即使允许归约中存在某些错误，Leaf也不能归约到OntoWeakPigeon。