Neighbourhood semantics for intuitionistic logic extended with countable conjunctions and disjunctions is introduced and shown equivalent to topological semantics, with an indirect completeness proof as payoff. The new semantics is used to obtain a labelled sequent calculus with good structural properties. In particular, admissibility of weakening and contraction, invertibility with preservation of height for each rule and cut elimination are shown. Finally, a direct Tait–Schütte–Takeuti style form of completeness via the extraction of a countermodel from a failed proof search is proved.

中文翻译：

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直觉无限逻辑的邻域语义和标记微积分

引入了用可数连词和析取词扩展的直觉逻辑的邻域语义，并显示其等效于拓扑语义，并以间接完整性证明作为回报。新语义用于获得具有良好结构特性的标记序列演算。特别是，显示了弱化和收缩的可接受性，每个规则的高度保持的可逆性和切割消除。最后，通过从失败的证明搜索中提取反模型，证明了直接的 Tait-Schütte-Takeuti 样式的完整性形式。