Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
A Lopez-Escobar theorem for continuous domains. / Bazhenov, Nikolay; Fokina, Ekaterina; Rossegger, Dino и др.
в: Journal of Symbolic Logic, 2024.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - A Lopez-Escobar theorem for continuous domains
AU - Bazhenov, Nikolay
AU - Fokina, Ekaterina
AU - Rossegger, Dino
AU - Soskova, Alexandra
AU - Vatev, Stefan
PY - 2024
Y1 - 2024
N2 - We prove an effective version of the Lopez-Escobar theorem for continuous domains. Let Mod(τ) be the set of countable structures with universe ω in vocabulary τ topologized by the Scott topology. We show that an invariant set X ⊆ Mod(τ) is Π0α in the effective Borel hierarchy of this topology if and only if it is definable by a Πpα-formula, a positive Π0α formula in the infinitary logic Lω1ω. As a corollary of this result we obtain a new pullback theorem for positive computable embeddings: Let K be positively computably embeddable in K′ by Φ, then for every Πpα formula ξ in the vocabulary of K′ there is a Πpα formula ξ∗ in the vocabulary of K such that for all A ∈ K, A |= ξ∗ if and only if Φ(A) |= ξ. We use this to obtain new results on the possibility of positive computable embeddings into the class of linear orderings.
AB - We prove an effective version of the Lopez-Escobar theorem for continuous domains. Let Mod(τ) be the set of countable structures with universe ω in vocabulary τ topologized by the Scott topology. We show that an invariant set X ⊆ Mod(τ) is Π0α in the effective Borel hierarchy of this topology if and only if it is definable by a Πpα-formula, a positive Π0α formula in the infinitary logic Lω1ω. As a corollary of this result we obtain a new pullback theorem for positive computable embeddings: Let K be positively computably embeddable in K′ by Φ, then for every Πpα formula ξ in the vocabulary of K′ there is a Πpα formula ξ∗ in the vocabulary of K such that for all A ∈ K, A |= ξ∗ if and only if Φ(A) |= ξ. We use this to obtain new results on the possibility of positive computable embeddings into the class of linear orderings.
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85187989028&origin=inward&txGid=83f10de026675972dd10c2de1eeb9aee
UR - https://www.mendeley.com/catalogue/ca900d02-c6a6-38a2-9eb0-cc50bfb44550/
U2 - 10.1017/jsl.2024.18
DO - 10.1017/jsl.2024.18
M3 - Article
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
SN - 1943-5886
ER -
ID: 60477163