On some connections between Boolean algebras and Heyting algebras
Dimitrii E. Pal'chunov, Alain Touraille (1992)
Annales scientifiques de l'Université de Clermont. Mathématiques
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Dimitrii E. Pal'chunov, Alain Touraille (1992)
Annales scientifiques de l'Université de Clermont. Mathématiques
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Sabine Koppelberg (1988)
Acta Universitatis Carolinae. Mathematica et Physica
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Abad Manuel, Cimadamore Cecilia, Díaz Varela José (2009)
Open Mathematics
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In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.
F. M. Sioson (1965-1966)
Compositio Mathematica
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Radim Bělohlávek (2003)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Paul Iverson (1991)
Colloquium Mathematicae
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There is a conjecture of Vaught [17] which states: Without The Generalized Continuum Hypothesis one can prove the existence of a complete theory with exactly nonisomorphic, denumerable models. In this paper we show that there is no such theory in the class of complete extensions of the theory of Boolean algebras. More precisely, any complete extension of the theory of Boolean algebras has either 1 or nonisomorphic, countable models. Thus we answer this conjecture in the negative...