PreprintCC BY 4.0arXiv
Dependent choice and iterated beta_n-model reflection
Abstract
In this paper, we consider conservation results for iterated βn-model reflection principles. Using these principles, we characterize the Π1m+2-, Σ1m+2- and B(Π1m+2)-consequences of Σ1n+1-DC0 and Σ1n+1-TDC0 for m ≤ n. Here, B(Π1m+2) denotes the set of Boolean combinations of Π1m+2-formulas, and TDC stands for transfinite DC. We also show that, in each case, the stronger theory has a super-exponential speed-up over the corresponding conservative subtheory.
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BibTeX
@misc{suzuki2026dependent,
title = {{Dependent choice and iterated beta_n-model reflection}},
author = {Yudai Suzuki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36982},
eprint = {2610.36982},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36982},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dependent choice and iterated beta_n-model reflection
AU - Yudai Suzuki
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36982
UR - https://arxiv.org/abs/2610.36982
AB - In this paper, we consider conservation results for iterated β_n-model reflection principles. Using these principles, we characterize the Π^1_m+2-, Σ^1_m+2- and B(Π^1_m+2)-consequences of Σ^1_n+1-DC_0 and Σ^1_n+1-TDC_0 for m ≤ n. Here, B(Π^1_m+2) denotes the set of Boolean combinations of Π^1_m+2-formulas, and TDC stands for transfinite DC. We also show that, in each case, the stronger theory has a super-exponential speed-up over the corresponding conservative subtheory.
ER -