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Categoricity of theories in Lκω , when κ is a measurable cardinal. Part 1

Saharon Shelah, Oren Kolman (1996)

Fundamenta Mathematicae

We assume a theory T in the logic L κ ω is categorical in a cardinal λ κ, and κ is a measurable cardinal. We prove that the class of models of T of cardinality < λ (but ≥ |T|+κ) has the amalgamation property; this is a step toward understanding the character of such classes of models.

Categoricity without equality

H. Jerome Keisler, Arnold W. Miller (2001)

Fundamenta Mathematicae

We study categoricity in power for reduced models of first order logic without equality.

Cauchy-like functional equation based on a class of uninorms

Feng Qin (2015)

Kybernetika

Commuting is an important property in any two-step information merging procedure where the results should not depend on the order in which the single steps are performed. In the case of bisymmetric aggregation operators with the neutral elements, Saminger, Mesiar and Dubois, already reduced characterization of commuting n -ary operators to resolving the unary distributive functional equations. And then the full characterizations of these equations are obtained under the assumption that the unary...

Cayley's Theorem

Artur Korniłowicz (2011)

Formalized Mathematics

The article formalizes the Cayley's theorem saying that every group G is isomorphic to a subgroup of the symmetric group on G.

Cellularity of free products of Boolean algebras (or topologies)

Saharon Shelah (2000)

Fundamenta Mathematicae

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 ω λ = c f ( λ ) 2 μ then 𝔹 satisfies the λ-Knaster condition (using the “revised GCH theorem”).

Certain partitions on a set and their applications to different classes of graded algebras

Antonio J. Calderón Martín, Boubacar Dieme (2021)

Communications in Mathematics

Let ( 𝔄 , ϵ u ) and ( 𝔅 , ϵ b ) be two pointed sets. Given a family of three maps = { f 1 : 𝔄 𝔄 ; f 2 : 𝔄 × 𝔄 𝔄 ; f 3 : 𝔄 × 𝔄 𝔅 } , this family provides an adequate decomposition of 𝔄 { ϵ u } as the orthogonal disjoint union of well-described -invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak H * -algebras.

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