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- W4287670072 abstract "We adjust the notion of finitary filter pair, which was coined for creating and analyzing finitary logics, in such a way that we can treat logics of cardinality $kappa$, where $kappa$ is a regular cardinal. The corresponding new notion is called $kappa$-filter pair. A filter pair can be seen as a presentation of a logic, and we ask what different $kappa$-filter pairs give rise to a fixed logic of cardinality $kappa$. To make the question well-defined we restrict to a subcollection of filter pairs and establish a bijection from that collection to the set of natural extensions of that logic by a set of variables of cardinality $kappa$. Along the way we use $kappa$-filter pairs to construct natural extensions for a given logic, work out the relationships between this construction and several others proposed in the literature, and show that the collection of natural extensions forms a complete lattice. In an optional section we introduce and motivate the concept of a general filter pair." @default.
- W4287670072 created "2022-07-25" @default.
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- W4287670072 date "2020-09-09" @default.
- W4287670072 modified "2023-09-23" @default.
- W4287670072 title "Filter pairs and natural extensions of logics" @default.
- W4287670072 doi "https://doi.org/10.48550/arxiv.2009.04377" @default.
- W4287670072 hasPublicationYear "2020" @default.
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