Positively closed Sh(B)-valued models

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2026-06-01 Epub Date: 2026-01-28 DOI:10.1016/j.apal.2026.103726

Kristóf Kanalas

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引用次数: 0

Abstract

We study positively closed and strongly positively closed topos-valued models of coherent theories. Positively closed is a global notion (it is defined in terms of all possible outgoing homomorphisms), while strongly positively closed is a local notion (it only concerns the definable sets inside the model). For Set-valued models of coherent theories they coincide.

We prove that if

E = S h (B, τ_{c o h})

for a complete Boolean algebra, then positively closed but not strongly positively closed

E

-valued models of coherent theories exist, yet, there is an alternative local property which characterizes positively closed

E

-valued models.

A large part of our discussion is given in the context of infinite quantifier geometric logic, dealing with the fragment

L_{κ κ}^{g}

where κ is weakly compact.

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正闭Sh(B)值模型

我们研究了相干理论的正闭和强正闭拓扑值模型。正闭是一个全局概念（它是根据所有可能的外向同态定义的），而强正闭是一个局部概念（它只涉及模型内的可定义集合）。对于相干理论的集值模型，它们是一致的。我们证明了对于完全布尔代数，如果E=Sh(B,τcoh)，则相干理论的正闭但不是强正闭E值模型存在，然而，存在表征正闭E值模型的另一种局部性质。我们的大部分讨论是在无限量词几何逻辑的背景下给出的，处理片段Lκκg，其中κ是弱紧的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.