Answering an open question raised by Cooper, we show that there exist Δ-0-2 sets D and E such that the singleton degree of E is a minimal cover of the singleton degree of D. This shows that the Σ0-2 singleton degrees, and the Δ0-2 singleton degrees, are not dense (and consequently the Π-0-2 Q-degrees, and the Δ-0-2 Q-degrees, are not dense). Moreover, D and E can be built to lie in the same enumeration degree.}

Kent, T.F., Meng Ng, K., Sorbi, A. (2025). The singleton degrees of the Sigma-0-2 sets are not dense. ANNALS OF PURE AND APPLIED LOGIC, 176(9), 1-16 [10.1016/j.apal.2025.103616].

The singleton degrees of the Sigma-0-2 sets are not dense

Andrea Sorbi
2025-01-01

Abstract

Answering an open question raised by Cooper, we show that there exist Δ-0-2 sets D and E such that the singleton degree of E is a minimal cover of the singleton degree of D. This shows that the Σ0-2 singleton degrees, and the Δ0-2 singleton degrees, are not dense (and consequently the Π-0-2 Q-degrees, and the Δ-0-2 Q-degrees, are not dense). Moreover, D and E can be built to lie in the same enumeration degree.}
2025
Kent, T.F., Meng Ng, K., Sorbi, A. (2025). The singleton degrees of the Sigma-0-2 sets are not dense. ANNALS OF PURE AND APPLIED LOGIC, 176(9), 1-16 [10.1016/j.apal.2025.103616].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1296134