An interpolation theorem

连续Craig插值

Continuous Craig Interpolation

该研究在度量结构的连续模型论领域，证明了与Craig插值定理相对应的类似结论，拓展了连续模型论的插值理论相关成果。

分裂插值：通过三值逻辑精化克雷格定理

Split Interpolation: Refining Craig's Theorem via Three-Valued Logics

本文研究三值逻辑下分裂插值性质成立的条件，确定了基于相同三值布尔正规单调方案和单调推论关系的逻辑对满足该性质的情形，从而精化了克雷格插值定理。

On Weak and Strong Interpolation in Algebraic Logics

We show that there is a restriction, or modification of the finite-variable fragments of First Order Logic in which a weak form of Craig's Interpolation Theorem holds, but a strong form of this theorem does not hold. Translating these results into Algebraic Logic we obtain a finitely axiomatizable subvariety of finite dimensional Representable Cylindric Algebras that has the Strong Amalgamation Property, but does not have the Superamalgamation Property. This settles a conjecture of Pigozzi

Craig插值定理在双直觉谓词逻辑中不成立

Craig interpolation theorem fails in bi-intuitionistic predicate logic

本文通过改编Mints等人的反例，证明双直觉谓词逻辑缺乏Craig插值性质，并澄清该结果与Rauszer的“演绎插值”定理不矛盾。

Nice infinitary logics

Ordinary infinitary languages L_{lambda, kappa} satisfy the Interpolation Theorem only in the case lambda <= {aleph_1}, kappa = {aleph_0}, this include first order logic of course. There are also some pairs of such logics satifying interpolation, e.g. (L_{lambda^+,{aleph_0}}, L_{(2^lambda)^+, lambda^+}) . Does this come from an intermidiate logic satisfying it? Is it nice? unique? We define for kappa = beth_kappa a new logic L^1_kappa such that L_{kappa omega}< L^1_kappa LL_{kappa kappa} and L^1_kappa is very nice; in particular satisfies the Interpolation Theorem. Moreover, L^1_kappa has a mo…

统一插值

Uniform Interpolation

本文通过Pitts定理，利用对偶性语义证明直觉主义命题逻辑的统一插值性质，并推广到Esakia空间的开映射定理，探讨其在范畴逻辑、代数和模型论中的联系。