### Abstract

In this paper a structure of a syslem is defined as a mathematical structure [formula omitted], where [formula omitted]is a first-order logic language and Σ is a set of sentences of the given first-order logic. It is shown that a canonical structure determined by I, which is similar to those used in proving the Gödel's completeness theorem, satisfies a universality in the sense of category theory when homomorphisms are used as morphisms, and a freeness in the sense of universal algebra when Σ-morphisms, which preserve Σ, are used. The universality and the freeness give the minimality of the canonical structure.As an example, a structure of a stationary system is defined as a pair [formula omitted] Its canonical structure is actually constructed. In a sense this canonical structure accords with models constructed by Nerode realization.

Original language | English |
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Pages (from-to) | 141-163 |

Number of pages | 23 |

Journal | International Journal of General Systems |

Volume | 15 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1989 |

Externally published | Yes |

### Keywords

- canonical structure
- freeness
- language
- minimality
- model
- stationary system
- Structure
- universality

### ASJC Scopus subject areas

- Computer Science Applications
- Control and Systems Engineering
- Modelling and Simulation
- Theoretical Computer Science
- Information Systems

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## Cite this

*International Journal of General Systems*,

*15*(2), 141-163. https://doi.org/10.1080/03081078908935038