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# Canonical structure in the universe of set theory: part two

@article{Cummings2006CanonicalSI, title={Canonical structure in the universe of set theory: part two}, author={James Cummings and Matthew Foreman and Menachem Magidor}, journal={Ann. Pure Appl. Logic}, year={2006}, volume={142}, pages={55-75} }

- Published 2006 in Ann. Pure Appl. Logic
DOI:10.1016/j.apal.2005.11.007

We start by studying the relationship between two invariants isolated by Shelah, the sets of good and approachable points. As part of our study of these invariants, we prove a form of “singular cardinal compactness” for Jensen’s square principle. We then study the relationship between internally approachable and tight structures, which parallels to a certain extent the relationship between good and approachable points. In particular we characterize the tight structures in terms of PCF theory… CONTINUE READING

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