Moore introduced the Mapping Reflection Principle and proved that the Bounded Proper Forcing Axiom implies that the size of the continuum is \(\aleph _2\). The Mapping Reflection Principle follows from the Proper Forcing Axiom. To show this, Moore utilized forcing notions whose conditions are countable objects. Chodounský–Zapletal introduced the Y-Proper Forcing Axiom that is a weak fragments of the Proper Forcing Axiom but implies some important conclusions from the Proper Forcing Axiom, for example, the P-ideal Dichotomy. In this article, it is proved that the Y-Proper Forcing Axiom implies the Mapping Reflection Principle by introducing forcing notions whose conditions are finite objects.

Moore引入了映射反射原理，并证明了有界正确强迫公理意味着连续体的大小为\（\ aleph _2 \）。映射反射原理遵循正确的强制公理。为了说明这一点，摩尔利用了条件为可数对象的强制概念。Chodounský-Zapletal引入了Y-Proper强迫公理，它是Proper强迫公理的一个弱片段，但它暗示了Proper强迫公理的一些重要结论，例如P-理想二分法。在本文中，通过引入条件为有限对象的强迫概念，证明了Y-适当强迫公理暗含了映射反射原理。