In this paper, new methods for analyzing models of weak subsystems of Peano Arithmetic are proposed. The focus will be on the study of algebro-combinatoric properties of certain definable cuts. Their relationship with segments that satisfy more induction, with those limited by the standard powers/roots of an element, and also with definable sets in Bounded Induction is studied. As a consequence, some considerations on the ${\mathrm{\Pi }}_1$-interpretability of $\mathrm{\text{I}}{\mathrm{\Delta }}_0$ in weak theories, as well as some alternative axiomatizations, are reviewed. Some of the results of the paper are obtained by immersing Bounded Induction models in its Stone-Cech Compactification, once it is endowed with a topology.

本文提出了一种新的分析Peano算法弱子系统模型的方法。重点将放在某些可定义切割的代数组合性质的研究上。研究了它们与满足更多归纳法的段，受元素的标准幂/根限制的段之间的关系，以及与有界归纳法中的可定义集的关系。因此，关于${\mathrm{\Pi }}_{\mathrm{1个}}$-的可解释性 $\mathrm{\text{一世}}{\mathrm{\Delta }}_0$在薄弱的理论，以及一些替代公理化，进行了审查。本文的某些结果是通过将有界归纳模型浸入其Stone-Cech压实结构中而获得的，该模型具有拓扑结构。