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Notes on Free Monadic Boolean Algebras
Order, 1999The authors provide a new construction of the free monadic Boolean algebra on \(n\) generators. The proof involves numerous lemmas which generalize previous results of \textit{H. Bass} [Proc. Am. Math. Soc. 9, 258-268 (1958; Zbl 0089.01904)].
Luiz F. Monteiro +3 more
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On functions defined on free Boolean algebras
Proceedings 32nd IEEE International Symposium on Multiple-Valued Logic, 2002We characterize measures on free Boolean algebras and we examine the relationships that exists between measures and binary tables in relational databases. It is shown that these measures are completely defined by their values on positive conjunctions and an algorithm that leads to the construction of measures starting from its values on a positive ...
Ivo G. Rosenberg +2 more
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Freely generated filters in free Boolean algebras
Studia Logica, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Free algebras in varieties of BL-algebras with a Boolean retract.
Algebra Universalis, 2002BL-algebras, introduced by \textit{P.\ Hájek} [Metamathematics of fuzzy logic. Trends in Logic -- Studia Logica Library 4, Kluwer Academic Publishers, Dordrecht (1998; Zbl 0937.03030)], are an algebraic counterpart of basic fuzzy logic. It is known that BL-algebras form a variety of residuated lattices or residuated \(\ell \)-monoids.
Cignoli, Roberto, Torrens, Antoni
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Atom-free ideals of constructive boolean algebras
Algebra and Logic, 1984A denumerable structure is said to be recursive if its universe is a recursive subset of the set of natural numbers and its relations and operations are recursive. A structure is said to be recursively presentable if it is isomorphic to a recursive structure. \textit{L. Feiner} [J. Symb.
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Elementary theories of free topo-Boolean and pseudo-Boolean algebras
Mathematical Notes of the Academy of Sciences of the USSR, 1985As is well known there exists a dual isomorphism between the lattice of extensions of the modal logic S4 (the intuitionistic logic Int) and the lattice of varieties of topo-Boolean (pseudo-Boolean) algebras assigning to a logic \(\lambda\) the variety algebras var(\(\lambda)\).
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Mardešić conjecture and free products of Boolean algebras
2017We show that for every $d\ge 1$, if $L_1,\ldots, L_d$ are linearly ordered compact spaces and there is a continuous surjection \[ L_1\times L_2\times \dots\times L_d\to K_1\times K_2\times\ldots\times K_{d}\times K_{d+1},\] where all the spaces $K_i$ are infinite, then $K_i, K_j$ are metrizable for some $1\le ...
Martínez-Cervantes, Gonzalo +1 more
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On the nonexistence of free complete Boolean algebras
1962Rieger asked in 1951 if there exists a free complete Boolean algebra on ω complete generators. Crawley and Dean proved in 1955 that there does not exist a free complete lattice on three complete generators, but their method does not extend to Boolean algebras. In this thesis Rieger's question is answered in the negative.
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A Solution of the Word Problem for Free Double Boolean Algebras
2007Double Boolean algebras were introduced in [Wi00a] as a variety fundamental for Boolean Concept Logic, an extension of Formal Concept Analysis allowing negations of formal concepts. In this paper, the free double Boolean algebra generated by the constants is described. Moreover, we show that every free double Boolean algebra with at least one generator
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