Weak Kurepa trees, slender tree properties, and guessing models, part 1

The weak Kurepa hypothesis at omega_1 says that there exists a tree of size and height omega_1 which has at least omega_2 many cofinal branches. In the talk we will focus on the negation of the weak Kurepa hypothesis and the connection to the slender tree and ineffable slender tree properties at omega_2.

In the first part of the talk(s) we will focus on the negation of the weak Kurepa hypothesis and its effect on cardinal arithmetic. In the second part of the talk(s) we define the slender tree property and show that the slender tree property implies the negation of weak Kurepa hypothesis. In the last part of the talk(s) we will define the guessing model principle at omega_2 and its variants and compare them with the slender tree properties.