Displaying similar documents to “On the existence of prime ideals in Boolean algebras”

Program Algebra over an Algebra

Grzegorz Bancerek (2012)

Formalized Mathematics

Similarity:

We introduce an algebra with free variables, an algebra with undefined values, a program algebra over a term algebra, an algebra with integers, and an algebra with arrays. Program algebra is defined as universal algebra with assignments. Programs depend on the set of generators with supporting variables and supporting terms which determine the value of free variables in the next state. The execution of a program is changing state according to successor function using supporting terms. ...

The number of countable isomorphism types of complete extensions of the theory of Boolean algebras

Paul Iverson (1991)

Colloquium Mathematicae

Similarity:

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 ω 1 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 2 ω nonisomorphic, countable models. Thus we answer this conjecture in the negative...

A model theory approach to structural limits

Jaroslav Nešetřil, Patrice Ossona de Mendez (2012)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an example, we generalize limits of bounded degree graphs from subgraph testing to finite model testing.

On connections between information systems, rough sets and algebraic logic

Stephen Comer (1993)

Banach Center Publications

Similarity:

In this note we remark upon some relationships between the ideas of an approximation space and rough sets due to Pawlak ([9] and [10]) and algebras related to the study of algebraic logic - namely, cylindric algebras, relation algebras, and Stone algebras. The paper consists of three separate observations. The first deals with the family of approximation spaces induced by the indiscernability relation for different sets of attributes of an information system. In [3] the family of closure...