I gave an invited talk at the P.O.I Workshop in pure and descriptive set theory, Torino, September 26, 2015.

** Title:** $\aleph_3$-trees.

**Abstract:** We inspect the constructions of four quite different $\aleph_3$-Souslin trees.

**Downloads:**

papers, preprints, slides and expository

I gave an invited talk at the P.O.I Workshop in pure and descriptive set theory, Torino, September 26, 2015.

** Title:** $\aleph_3$-trees.

**Abstract:** We inspect the constructions of four quite different $\aleph_3$-Souslin trees.

**Downloads:**

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after my talk, David Aspero was referring to page #103 of my slides, asking why do we appeal to fine structure, where we could also use forcing to obtain the relevant combinatorial objects.

It took me a few minutes to find the right answer (the spontaneous one was – “I just like L”). The deeper answer is that we actually appeal to L to help us *formulate* the right principle. After all, there is no obvious way for a principle combining square and diamond-plus to be defined. It is the iterative process of defining/trying-to-prove-in-L/revisiting-the-definition/retrying-to-prove-in-L/etc’ that led to the “right” definition.

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