Non-reversibility of the implication from SCC^cof to SCC^split

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Let SCCcof\text{SCC}^{\text{cof}} and SCCsplit\text{SCC}^{\text{split}} denote the two set-theoretic principles introduced in the surrounding discussion. Non-reversibility conjecture. The implication

SCCcof  ⟹  SCCsplit\text{SCC}^{\text{cof}} \implies \text{SCC}^{\text{split}}

is not reversible; that is, SCCsplit\text{SCC}^{\text{split}} does not imply SCCcof\text{SCC}^{\text{cof}}. This concerns the relative strength of two variants of Strong Chang's Conjecture. The surrounding text states that the reversibility of the remaining implications under consideration is open, and motivates this conjecture using characterizations of the two principles by Shelah and by Cox and Sakai.

References

Primary source

Sean Cox, “Adjoining only the things you want: a survey of Strong Chang's Conjecture and related topics”, arXiv:1908.05334 (2020).

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