Program Algebra over an Algebra

Grzegorz Bancerek

Displaying similar documents to “Program Algebra over an Algebra”

On positive, linear and quadratic Boolean functions

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Analysis of Algorithms: An Example of a Sort Algorithm

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We analyse three algorithms: exponentiation by squaring, calculation of maximum, and sorting by exchanging in terms of program algebra over an algebra.

The Nikodym property and local properties of Boolean algebras

Antonio Aizpuru (1996)

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We study local interpolation properties and local supremum properties for a Boolean algebra. In particular, we present a new condition that is sufficient for the Nikodym property.

On the existence of prime ideals in Boolean algebras

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Rasiowa and Sikorski [5] showed that in any Boolean algebra there is an ultrafilter preserving countably many given infima. In [3] we proved an extension of this fact and gave some applications. Here, besides further remarks, we present some of these results in a more general setting.

A basis of the conjunctively polynomial-like Boolean functions.

Gonda, J. (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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A model theory approach to structural limits

Jaroslav Nešetřil, Patrice Ossona de Mendez (2012)

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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 the implementation of set-valued non-Boolean functions.

Čomić, Lidija, Tošić, Ratko (2004)

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First Order Languages: Further Syntax and Semantics

Marco Caminati (2011)

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Third of a series of articles laying down the bases for classical first order model theory. Interpretation of a language in a universe set. Evaluation of a term in a universe. Truth evaluation of an atomic formula. Reassigning the value of a symbol in a given interpretation. Syntax and semantics of a non atomic formula are then defined concurrently (this point is explained in [16], 4.2.1). As a consequence, the evaluation of any w.f.f. string and the relation of logical implication are...

Conjunctively polynomial-like Boolean functions.

Gonda, J. (2007)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Cellularity of free products of Boolean algebras (or topologies)

Saharon Shelah (2000)

Fundamenta Mathematicae

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The aim this paper is to present an answer to Problem 1 of Monk [10], [11]. We do this by proving in particular that if μ is a strong limit singular cardinal, $θ = {(2^{c f (μ)})}^{+}$ and $2^{μ} = μ^{+}$ then there are Boolean algebras $𝔹_{1}, 𝔹_{2}$ such that $c (𝔹_{1}) = μ, c (𝔹_{2}) < θ b u t c (𝔹_{1} * 𝔹_{2}) = μ^{+}$ . Further we improve this result, deal with the method and the necessity of the assumptions. In particular we prove that if $𝔹$ is a ccc Boolean algebra and $μ^{ℶ_{ω}} \leq λ = c f (λ) \leq 2^{μ}$ then $𝔹$ satisfies the λ-Knaster condition (using the “revised GCH theorem”).