Constructibility real degrees in the side-by-side Sacks model

2025/04/07 by Notaro, Lorenzo · 1 citation
#FOS: Mathematics #Logic (math.LO) #Primary 03E35 #Secondary 03E45

paper · doi:10.48550/arxiv.2504.04902

Abstract

We study the join-semilattice of constructibility real degrees in the side-by-side Sacks model, the model of set theory obtained by forcing with a countable-support product of infinitely many Sacks forcings over the constructible universe. In particular, we prove that in the side-by-side Sacks model the join-semilattice of constructibility real degrees is rigid, i.e. it does not have non-trivial automorphisms.

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• Σ¹₃ sets in the Sacks model

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