## Past Seminars- Logic Set Theory

• Grigor Sargsyan
Mon May 16, 2016
4:00 pm
We will compute the mantle, the intersection of all grounds, of the minimal class size mouse with a Woodin cardinal and a Strong cardinal.
• Garrett Ervin
Mon May 9, 2016
4:00 pm
We complete the proof of the main theorem by showing that if X^3 is isomorphic to X, then X^{\omega} has a parity-reversing automorphism. By our previous results this implies X^2 is isomorphic to X as well. The proof generalizes to show that for any n > 1, if X^n is isomorphic to X, then X^2 is isomorphic to X. Time permitting we will discuss...
• Dima Sinapova
Mon May 2, 2016
4:00 pm
A remarkable theorem of Shelah states that if $\kappa$ is a singular strong limit cardinal of uncountable cofinality, then there is a subset $x$ of $\kappa$, such that $HOD_x$ contains the powerset of $\kappa$. We show that in general this is not  the case for countable cofinality. Using a version of diagonal supercompact extender Prikry...
• Garrett Ervin
Mon Apr 25, 2016
4:00 pm
We complete the proof of the main theorem by showing that if X^3 is isomorphic to X, then X^{\omega} has a parity-reversing automorphism. By our previous results this implies X^2 is isomorphic to X as well. The proof generalizes to show that for any n > 1, if X^n is isomorphic to X, then X^2 is isomorphic to X. Time permitting we will discuss...
• Garrett Ervin
Mon Apr 18, 2016
4:00 pm
Our eventual goal is to see that if X is any linear order that isomorphic to its cube, then X^{\omega} has a parity-reversing automorphism. Then by the results of last week, X will also be isomorphic to its square. This week, I will describe a method for building partial parity-reversing automorphisms on any A^{\omega}, and give structural...
• Garrett Ervin
Mon Apr 11, 2016
4:00 pm
Building on our characterization from last week of the orders X that are isomorphic to AX, we characterize those X that are isomorphic to AAX. We then write down a condition -- namely, the existence of a parity-reversing automorphism (p.r.a.) for the countable power of A -- under which the implication AAX = X implies AX = X" holds. In...
• Garrett Ervin
Mon Apr 4, 2016
4:00 pm
We continue toward a proof of the main theorem by characterizing, for a fixed linear order A, the collection of linear orders X such that AX is isomorphic to X, finishing the argument we started with the last time.