Standard

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 изданияхстатьяРецензирование

Harvard

Bazhenov, N, Fokina, E, Rossegger, D, Soskova, A & Vatev, S 2024, 'A Lopez-Escobar theorem for continuous domains', Journal of Symbolic Logic. https://doi.org/10.1017/jsl.2024.18

APA

Bazhenov, N., Fokina, E., Rossegger, D., Soskova, A., & Vatev, S. (2024). A Lopez-Escobar theorem for continuous domains. Journal of Symbolic Logic. https://doi.org/10.1017/jsl.2024.18

Vancouver

Bazhenov N, Fokina E, Rossegger D, Soskova A, Vatev S. A Lopez-Escobar theorem for continuous domains. Journal of Symbolic Logic. 2024. doi: 10.1017/jsl.2024.18

Author

Bazhenov, Nikolay ; Fokina, Ekaterina ; Rossegger, Dino и др. / A Lopez-Escobar theorem for continuous domains. в: Journal of Symbolic Logic. 2024.

BibTeX

@article{1482eba0bcfc4c63a12ef3c41cdb7ddd,
title = "A Lopez-Escobar theorem for continuous domains",
abstract = "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.",
author = "Nikolay Bazhenov and Ekaterina Fokina and Dino Rossegger and Alexandra Soskova and Stefan Vatev",
year = "2024",
doi = "10.1017/jsl.2024.18",
language = "English",
journal = "Journal of Symbolic Logic",
issn = "1943-5886",

}

RIS

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