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

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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Publication Details

Journal
Annals of Pure and Applied Logic
Published
2026-01-08
DOI
https://doi.org/10.1016/j.apal.2026.103722
Primary Topic
Advanced Topology and Set Theory
Type
article
Field-Weighted Citation Impact
0.00

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article

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

Lorenzo Notaro
Annals of Pure and Applied Logic
Advanced Topology and Set Theory
article

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

Lorenzo Notaro
article en

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.

Annals of Pure and Applied LogicVol. 177(5)
Istituto Nazionale di Alta Matematica "Francesco Severi"
Openalex Percentile: Top 97%
Advanced Topology and Set Theory
DOIOpen Access PDFOpenAlex
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Constructibility real degrees in the side-by-side Sacks model — Lorenzo Notaro · Annals of Pure and Applied Logic (2026) | TGRS Research Map | TGRS