Results 61 to 70 of about 111 (106)
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Ultraproducts in the Theory of Models
The Annals of Mathematics, 1961In this paper we shall study an algebraic construction which has become a powerful new tool in the theory of models.1 This construction, called the ultraproduct operation', was first described in Los [20] under the name "champ logique," where its characteristic property of yielding elementary extensions of a given relational system was stated.
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2020
The goal of this chapter is to show that every consistent L-theory has a model, no matter whether the signature L is countable or uncountable.
Lorenz Halbeisen, Regula Krapf
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The goal of this chapter is to show that every consistent L-theory has a model, no matter whether the signature L is countable or uncountable.
Lorenz Halbeisen, Regula Krapf
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Complete Boolean ultraproducts
Journal of Symbolic Logic, 1987Throughout this paper, B will always be a Boolean algebra and Γ an ultrafilter on B. We use + and Σ for the Boolean join operation and · and Π for the Boolean meet.κ is always a regular cardinal. C(κ) is the full structure of κ, the structure with universe κ and whose functions and relations consist of all unitary functions and relations on κ.
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Ultraproducts which are not saturated
Journal of Symbolic Logic, 1967In this paper we continue our study, begun in [5], of the connection between ultraproducts and saturated structures. IfDis an ultrafilter over a setI, andis a structure (i.e., a model for a first order predicate logicℒ), the ultrapower ofmoduloDis denoted byD-prod.
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Journal of Symbolic Logic, 1967
It is shown in [1] that an ultraproduct of finite sets can be of arbitrarily large cardinality, but if it is infinite then it must have at least the power of the continuum. In this paper we shall take a closer look at the cardinality of ultraproducts of finite sets. Our results were announced without proof in [5].
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It is shown in [1] that an ultraproduct of finite sets can be of arbitrarily large cardinality, but if it is infinite then it must have at least the power of the continuum. In this paper we shall take a closer look at the cardinality of ultraproducts of finite sets. Our results were announced without proof in [5].
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Publicationes Mathematicae Debrecen, 2005
Summary: \textit{P. Bankston} [General Topology Appl. 7, 283--308 (1977; Zbl 0364.54005)] investigated ultraproducts of topological spaces and asked when the quotient mapping \(q:\square X_{\alpha } \rightarrow \square_{{\mathcal U} } X_{\alpha } \) is closed.
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Summary: \textit{P. Bankston} [General Topology Appl. 7, 283--308 (1977; Zbl 0364.54005)] investigated ultraproducts of topological spaces and asked when the quotient mapping \(q:\square X_{\alpha } \rightarrow \square_{{\mathcal U} } X_{\alpha } \) is closed.
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Institution-independent ultraproducts.
Fundam. Informaticae, 2003Summary: We generalise the ultraproducts method from conventional model theory to an institution-independent (i.e., independent of the details of the actual logic formalised as an institution) framework based on a novel, very general treatment of the semantics of some important concepts in logic, such as quantification, logical connectives, and ground ...
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General Topology and its Applications, 1977
We define a reduced product (in particular an ultraproduct) construction in topology which yields a class of quotients of the box product. Retention of certain properties under the formation of ultraproducts, as well as the role of ultraproducts in the study of zero dimensional spaces are investigated.
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We define a reduced product (in particular an ultraproduct) construction in topology which yields a class of quotients of the box product. Retention of certain properties under the formation of ultraproducts, as well as the role of ultraproducts in the study of zero dimensional spaces are investigated.
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1977
Publisher Summary The ultraproduct construction is an algebraic operation whose importance derives from its model-theoretic properties. The algebraic character of the construction makes it attractive tool to employ in giving an account of applications of model theory to algebra.
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Publisher Summary The ultraproduct construction is an algebraic operation whose importance derives from its model-theoretic properties. The algebraic character of the construction makes it attractive tool to employ in giving an account of applications of model theory to algebra.
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