Year: 2025
Type: preprint
Abstract: The purpose of the present paper is to analyze several variants of Solovay's theorem on the existence of doubly partially conservative sentences. First, we investigate $Θ$ sentences that are doubly $(Γ, Λ)$-conservative over $T$ for several triples $(Θ, Γ, Λ)$. Among other things, we prove that the existence of a $Δ_{n+1}(\mathsf{PA})$ sentence that is doubly $(Σ_n, Σ_n)$-conservative over $T$ is equivalent to the $Σ_{n+1}$-inconsistency of $T$ over $\mathsf{PA}$. Secondly, we study $Θ$ sentences that are hereditarily doubly $(Γ, Λ)$-conservative over $T$ for several triples $(Θ, Γ, Λ)$.
Source: arXiv (Cornell University)
Authors: Kogure, Haruka, Kurahashi, Taishi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6966809504
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