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Convergence and submeasures in Boolean algebras

Tomáš Jech (2018)

Commentationes Mathematicae Universitatis Carolinae

A Boolean algebra carries a strictly positive exhaustive submeasure if and only if it has a sequential topology that is uniformly Fréchet.

Didactical note: probabilistic conditionality in a Boolean algebra.

Enric Trillas, Claudi Alsina, Settimo Termini (1996)

Mathware and Soft Computing

This note deals with two logical topics and concerns Boolean Algebras from an elementary point of view. First we consider the class of operations on a Boolean Algebra that can be used for modelling If-then propositions. These operations, or Conditionals, are characterized under the hypothesis that they only obey to the Modus Ponens-Inequality, and it is shown that only six of them are boolean two-place functions. Is the Conditional Probability the Probability of a Conditional? This problem will...

Fuzzy n-fold integral filters in BL-algebras

Rajab Ali Borzooei, Akbar Paad (2013)

Discussiones Mathematicae - General Algebra and Applications

In this paper, we introduce the notion of fuzzy n-fold integral filter in BL-algebras and we state and prove several properties of fuzzy n-fold integral filters. Using a level subset of a fuzzy set in a BL-algebra, we give a characterization of fuzzy n-fold integral filters. Also, we prove that the homomorphic image and preimage of fuzzy n-fold integral filters are also fuzzy n-fold integral filters. Finally, we study the relationship among fuzzy n-fold obstinate filters, fuzzy n-fold integral filters...

Incomparable families and maximal trees

G. Campero-Arena, J. Cancino, M. Hrušák, F. E. Miranda-Perea (2016)

Fundamenta Mathematicae

We answer several questions of D. Monk by showing that every maximal family of pairwise incomparable elements of 𝒫(ω)/fin has size continuum, while it is consistent with the negation of the Continuum Hypothesis that there are maximal subtrees of both 𝒫(ω) and 𝒫(ω)/fin of size ω₁.

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