Andres Caicedo, associate professor of mathematics, will participate in the third meeting of the American Institute of Mathematics’ SQuaRE on “Descriptive aspects of inner model theory” May 20-24 in Palo Alto, Calif. SQuaRE stands for Structured Quartet Research Ensemble and it is a small, dedicated group of four to six mathematicians (in this case, it is six). Caicedo will spend a week at the AIM headquarters working on a specific research project. The other members of the group are Paul Larson (Miami University, Ohio), Grigor Sargsyan (Rutgers University), Ralf Schindler (University of Muenster), John Steel (University of California, Berkeley) and Martin Zeman (University of California, Irvine). Their collaboration already has resulted in a paper that will soon be published in the prestigious Israel Journal of Mathematics.
The group’s current focus is the question of whether fragments of “forcing axioms” can be recovered by the technique of forcing over models of determinacy. This work brings together several key areas of modern research in set theory. The paper, “Square principles in Pmax extensions,” shows that the answer is “yes” for some consequences of forcing axioms, namely, the nonexistence of so-called square sequences. A first version of the paper can be accessed at