### Abstract

In relation algebras, which model unweighted graphs, the cardinality operation counts the number of edges of a graph. We generalise the cardinality axioms to Stone relation algebras, which model weighted graphs, and study the relationships between various axioms for cardinality. We also give a representation theorem for Stone relation algebras.

### License

BSD License

### Topics

- Mathematics/Algebra

### Related publications

- Furusawa, H., & Guttmann, W. (2023). Cardinality and Representation of Stone Relation Algebras (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2309.11676

### Session Relational_Cardinality

- Representation
- Cardinality

### Depends on

- Infinite Lists
- Stone Relation Algebras

## Cite

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Relational_Cardinality-AFP

    @article{Relational_Cardinality-AFP,
      author  = {Walter Guttmann},
      title   = {Cardinality and Representation of Stone Relation Algebras},
      journal = {Archive of Formal Proofs},
      month   = {September},
      year    = {2023},
      note    = {\url{https://isa-afp.org/entries/Relational_Cardinality.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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