- Tytuł:
- A Category of Ordered Algebras Equivalent to the Category of Multialgebras
- Autorzy:
-
Coniglio, Marcelo Esteban
de Toledo, Guilherme Vicentin - Powiązania:
- https://bibliotekanauki.pl/articles/43182485.pdf
- Data publikacji:
- 2023
- Wydawca:
- Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
- Tematy:
-
multialgebras
ordered algebras
non-deterministic semantics - Opis:
- It is well known that there is a correspondence between sets and complete, atomic Boolean algebras CABAs) taking a set to its power-set and, conversely, a complete, atomic Boolean algebra to its set of atomic elements. Of course, such a correspondence induces an equivalence between the opposite category of Set and the category of CABAs. We modify this result by taking multialgebras over a signature Σ, specifically those whose non-deterministic operations cannot return the empty-set, to CABAs with their zero element removed (which we call a bottomless Boolean algebra) equipped with a structure of Σ-algebra compatible with its order (that we call ord-algebras). Conversely, an ord-algebra over Σ is taken to its set of atomic elements equipped with a structure of multialgebra over Σ. This leads to an equivalence between the category of Σ-multialgebras and the category of ord-algebras over Σ. The intuition, here, is that if one wishes to do so, non-determinism may be replaced by a sufficiently rich ordering of the underlying structures.
- Źródło:
-
Bulletin of the Section of Logic; 2023, 52, 4; 517-550
0138-0680
2449-836X - Pojawia się w:
- Bulletin of the Section of Logic
- Dostawca treści:
- Biblioteka Nauki
Artykuł