Opis

• Tytuł:
  A Category of Ordered Algebras Equivalent to the Category of Multialgebras
• Twórca:
  Coniglio, Marcelo Esteban;
  de Toledo, Guilherme Vicentin
• Współtwórca:
  Coniglio, Marcelo Esteban - University of Campinas (Unicamp), Institute of Philosophy and the Humanities (IFCH) and Centre for Logic, Epistemology and the History of Science (CLE)(UNICAMP);
  de Toledo, Guilherme Vicentin - Bar Ilan University, Department of Computer Science, The Spiegel Mathematics & Computer Center;
  Coniglio, Marcelo Esteban - coniglio@unicamp.br;
  de Toledo, Guilherme Vicentin - guivtoledo@gmail.com
• Opis:
  It is well known that there is a correspondence between sets and complete, atomic Boolean algebras (\(\textit{CABA}\)s) 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 \(\textbf{Set}\) and the category of \(\textit{CABA}\)s.We modify this result by taking multialgebras over a signature \(\Sigma\), specifically those whose non-deterministic operations cannot return the empty-set, to \(\textit{CABA}\)s with their zero element removed (which we call a \(\textit{bottomless Boolean algebra}\)) equipped with a structure of \(\Sigma\)-algebra compatible with its order (that we call \(\textit{ord-algebras}\)). Conversely, an ord-algebra over \(\Sigma\) is taken to its set of atomic elements equipped with a structure of multialgebra over \(\Sigma\). This leads to an equivalence between the category of \(\Sigma\)-multialgebras and the category of ord-algebras over \(\Sigma\).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.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa: https://creativecommons.org/licenses/by-nc-nd/4.0
• Data:
  2024.01.04;
  2023.08.16
• Typ:
  Other
• Język:
  angielski
• Format:
  application/pdf
• Wydawca:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relacja:
  Bulletin of the Section of Logic;4;
  52
• Temat i słowa kluczowe:
  multialgebras;
  ordered algebras;
  non-deterministic semantics
• Identyfikator:
  0138-0680;
  http://hdl.handle.net/11089/49161 ;
  2449-836X;
  10.18778/0138-0680.2023.23
• Dostawca danych:
  Repozytorium Uniwersytetu Łódzkiego
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