Realizing arbitrarily large spectra of $\mathfrak{a}_{\text{T}}$

Vera Fischer; Lukas Schembecker

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arXiv · 2312.10006

Realizing arbitrarily large spectra of $\mathfrak{a}_{\text{T}}$

Vera Fischer·Lukas Schembecker

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Abstract

We improve the state-of-the-art proof techniques for realizing various spectra of $\mathfrak{a}_{\text{T}}$ in order to realize arbitrarily large spectra. Thus, we make significant progress in addressing a question posed by Brian in his recent work. As a by-product, we obtain many complete subforcings and an algebraic analysis of the automorphisms of the forcing which adds a witness for the spectrum of $\mathfrak{a}_{\text{T}}$ of desired size.

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Vera Fischer, Lukas Schembecker. 2023-12-15. Realizing arbitrarily large spectra of $\mathfrak{a}_{\text{T}}$. https://arxiv.org/abs/2312.10006

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