These are the slides of a talk I gave at the Young Researchers in Set Theory 2011 meeting (Königswinter, 21–25 March 2011).

**Talk Title:** Around Jensen’s square principle

**Abstract**: Jensen‘s square principle for a cardinal $\lambda$ asserts the existence of a particular ladder system over $\lambda^+$.

This principle admits a long list of applications including the existence of non-reflecting stationary sets, and the existence of particular type of trees.

In this talk, we shall be concerned with the weaker principle, *weak square*, and the stronger principle, *Ostaszewski square*, and shall study their interaction with the classical applications of the square principle.

We shall isolate a non-reflection principle that follows from weak square, and discuss tree constructions based on Ostaszewski squares.

We shall present a rather surprising forcing notion that may (consistently) introduce weak square, and discuss a coloring theorem for pairs of ordinals, based on minimal walks along Ostaszewski squares.

**Downloads:**

**Updates:**

The first open problem from this presentation (slide 35) has been resolved. The solution may be found in here.