Completeness in local positive logic

Arturo Rodríguez Fanlo; Ori Segel

doi:10.1016/j.apal.2025.103601

Completeness in local positive logic

Arturo Rodríguez Fanlo^*
, Ori Segel

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We develop the basic model theory of local positive logic, a new logic that mixes positive logic (where negation is not allowed) and local logic (where models omit types of infinite distant pairs). We study several basic model theoretic notions such as compactness, positive closedness (existential closedness) and completeness (irreducibility).

Original language	English
Article number	103601
Journal	Annals of Pure and Applied Logic
Volume	176
Issue number	7
DOIs	https://doi.org/10.1016/j.apal.2025.103601
State	Published - Jul 2025

Bibliographical note

Publisher Copyright:
© 2025 Elsevier B.V.

Keywords

Local logic
Omitting types
Positive logic

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10.1016/j.apal.2025.103601License: CC BY-NC

Cite this

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title = "Completeness in local positive logic",

abstract = "We develop the basic model theory of local positive logic, a new logic that mixes positive logic (where negation is not allowed) and local logic (where models omit types of infinite distant pairs). We study several basic model theoretic notions such as compactness, positive closedness (existential closedness) and completeness (irreducibility).",

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AB - We develop the basic model theory of local positive logic, a new logic that mixes positive logic (where negation is not allowed) and local logic (where models omit types of infinite distant pairs). We study several basic model theoretic notions such as compactness, positive closedness (existential closedness) and completeness (irreducibility).

KW - Local logic

KW - Omitting types

KW - Positive logic

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AN - SCOPUS:105002289818

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VL - 176

JO - Annals of Pure and Applied Logic

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Completeness in local positive logic

Abstract

Bibliographical note

Keywords

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