Cofinitary groups and projective well-orders

Fuente: arXiv
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Autores principales: Fischer, Vera, Schembecker, Lukas, Schrittesser, David
Formato: Preprint
Publicado: 2023
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author Fischer, Vera
Schembecker, Lukas
Schrittesser, David
author_facet Fischer, Vera
Schembecker, Lukas
Schrittesser, David
contents We introduce the notion of a tight cofinitary group, which captures forcing indestructibility of maximal cofinitary groups for a long list of partial orders, including Cohen, Sacks, Miller, Miller partition forcing and Shelah's poset for diagonalizing maximal ideal. Introducing a new robust coding technique, we establish the relative consistency of $\mathfrak{a}_g=\mathfrak{d}<\mathfrak{c}=\aleph_2$ alongside the existence of a $Δ^1_3$-wellorder of the reals and a co-analytic witness for $\mathfrak{a}_g$.
format Preprint
id arxiv_https___arxiv_org_abs_2312_16618
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Cofinitary groups and projective well-orders
Fischer, Vera
Schembecker, Lukas
Schrittesser, David
Logic
We introduce the notion of a tight cofinitary group, which captures forcing indestructibility of maximal cofinitary groups for a long list of partial orders, including Cohen, Sacks, Miller, Miller partition forcing and Shelah's poset for diagonalizing maximal ideal. Introducing a new robust coding technique, we establish the relative consistency of $\mathfrak{a}_g=\mathfrak{d}<\mathfrak{c}=\aleph_2$ alongside the existence of a $Δ^1_3$-wellorder of the reals and a co-analytic witness for $\mathfrak{a}_g$.
title Cofinitary groups and projective well-orders
topic Logic
url https://arxiv.org/abs/2312.16618