The Hartogs–Lindenbaum spectrum of symmetric extensions

• Published in: Mathematical logic quarterly Vol. 70; no. 2; pp. 210 - 223
• Main Author: Ryan‐Smith, Calliope
• Format: Journal Article
• Language: English
• Published: Berlin Wiley Subscription Services, Inc 01.05.2024
• Subjects: Equivalence; Spectra

We expand the classic result that ACWO$\mathsf {AC}_\mathsf {WO}$ is equivalent to the statement “For all X$X$, ℵ(X)=ℵ∗(X)$\aleph (X)=\aleph ^*(X)$” by proving the equivalence of many more related statements. Then, we introduce the Hartogs–Lindenbaum spectrum of a model of ZF$\mathsf {ZF}$, and insp...