Combinatorial dichotomies in set theory

Bulletin of Symbolic Logic 17 (1):1-72 (2010)
We give an overview of a research line concentrated on finding to which extent compactness fails at the level of first uncountable cardinal and to which extent it could be recovered on some other perhaps not so large cardinal. While this is of great interest to set theorists, one of the main motivations behind this line of research is in its applicability to other areas of mathematics. We give some details about this and we expose some possible directions for further research
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DOI 10.2178/bsl/1294186662
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Dilip Raghavan (2013). P-Ideal Dichotomy and Weak Squares. Journal of Symbolic Logic 78 (1):157-167.
David Chodounský & Jindřich Zapletal (2015). Why Y-C.C. Annals of Pure and Applied Logic 166 (11):1123-1149.

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