I made some decent progress today research wise, although I am pretty tired from flying stand by yesterday. Although not super relevant, I figured out that the degree of Jonsson-ness I have been able to prove for the spaces so far is actually enough to guarantee that the algebraic version of the property is holding. In short, being omega-strongly Jonsson implies the algebraic property even without choice. I also fleshed out more of the Rowbottom properties for some of the combinations, and finished writing up some proofs for the combinations of length 3. I still don't feel like I'm hitting the right level of generality with my statements though.
I also got informed about the UCI summer school event by Cummings, and I went ahead and submitted for that. It would be a cool opportunity to see more of the axiom of choice side of the combinatorics I have been facing, and who knows, some of the pcf theory may prove useful. On the other hand, cofinalities are very complicated in L(R), and the best machinery I have seen to deal with them is the Jackson's theory of descriptions.
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