## Lukasiewicz-Moisil AlgebrasThe Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory. This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as &THgr;-algebras with negation. Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research. |

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### Contents

1 | |

Chapter 2 Topological Dualities in Lattice Theory | 83 |

Chapter 3 Elementary Properties of LukasiewiczMoisil Algebras | 105 |

Chapter 4 Connections With Other Classes of Lattices | 165 |

Chapter 5 Filters Ideals and vCongruences | 247 |

Chapter 6 Representation Theorems and Duality for LukasiewiczMoisilAlgebras | 285 |

Chapter 7 Categorical Properties of LukasiewiczMoisil Algebras | 359 |

Chapter 8 Monadic and Polyadic LukasiewiczMoisil Algebras | 417 |

Chapter 9 Lukasiewicz Logics | 459 |

Applications to Switching Theory | 539 |

551 | |

575 | |

579 | |

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algebra L E analytic tableau axioms axled Balbes and Dwinger bijection Boicescu Boolean algebra Cignoli complete complete lattice conditions are equivalent congruence constructed Corollary CT(X defined Definition denote distributive lattice Ds(L dual E C(L element endomorphisms epimorphism exists ﬁlter finite following conditions functor hence Heyting algebra homomorphism implies injective involution isomorphism L E LM19 L E LMn Lemma Let L E Lindenbaum-Tarski algebra LMi9 LMNi9 logic Lukasiewicz Lukasiewicz algebras Lukasiewicz-Moisil algebras m-complete Math maximal monadic Boolean algebras monomorphism Monteiro Morgan algebra morphism morphism f n-valued LM-algebra n-valued Moisil algebra n-valued Post algebra negation Notation obtain operations polyadic poset Priestley space prime filter Proof Prop(V Proposition propositional calculus prove pseudocomplemented r-algebra Remark satisfies semilattice similarly SpecL Stone algebra subalgebra subdirect subdirect product subset Suppose surjective Theorem unique