3/10/2016

I seem to have hit a snag when trying to make the range into R/E_0. I need to not only miss a non-smooth set, I need to miss its saturation. The non-smooth set is fine, but the saturation is troubling. This is a little trickier to extend than I first expected.

3/9/21016

The new method worked to show that the reals are strongly Jonsson. The proof is so much shorter! With some significant tweaking, this basic outline should work to show that E_0 is strongly Jonsson (or anything with a Mycielski property and countable equivalence classes really).

3/8/2016

It looks like we found a proof that R is strongly Jonsson that avoids using the canonization theorems. This is good news, especially for extending the result to E_0. The way we started looking at these tree constructions to get the Mycielski result really does elucidate the inherent combinatorics problem that these constructions boil down to. Talking to my roommate yesterday we decided that combinatorics is to set theory as matrix computations are to algebra.

3/6/2016

Put together the slides for my AMS sectional talk over the past couple days. I think I may need to trim a bit, but its looking pretty good. Tomorrow I start looking at the strong Jonsson property for E_0.

3/02/2016

Continued to write up Jonsson results today.

3/01/2016

I heard back for the North American ASL conference today. I applied too late and all the positions were already full. In the future I will have to be more on the ball. I submitted an abstract for the set theory graduate student meeting in new York today. That one should be pretty rewarding to go to.

No new research updates today, I just spent time organizing results.

2/29/2016

Good meeting with Jackson today. We confirmed my write up for the full Mycielski style result, and made a little more progress toward proving that R/E_0 is Jonsson. I need to push forward and try to get a canonization style result for the new maps we are considering.