**March 5**

**Hiroshi Sakai**,
Kobe University

**Generalized stationary reflection and cardinal arithmetic**

The stationary reflection principle, which is often called the Weak Reflection Principle, is known to have many interesting consequences. As for cardinal arithmetic, it implies that $\lambda^\omega = \lambda$ for all regular cardinal $\lambda \geq \omega_2$. In this talk, we will discuss higher analogues of this stationary reflection principle and their consequences on cardinal arithmetic.