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1 -Boolean spectrum, and stability

Piero Mangani, Annalisa Marcja (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dimostra che la conoscenza delle algebre di Boole dei definibili di modelli di cardinità 1 di una teoria elementare è sufficiente per decidere il suo tipo di stabilità.

𝐋 -embedding, Amalgamation and 𝐋 -elementary equivalence

Daniele Mundici (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Ogni logica L genera canonicamente la L -equivalenza L e la L -immersione 𝐿 proprio come la logica del primo ordine genera l’equivalenza elementare e l’immersione elementare . Astraendo da L , è interessante studiare in sè relazioni d’equivalenza e di immersione generali tra strutture. Mostriamo che esiste una corrispondenza biunivoca tra relazioni d’equivalenza con la proprietà di Robinson e relazioni d’immersione con la proprietà di Amalgamazione Forte ( A P + ). Caratterizziamo algebricamente quelle...

k -free separable groups with prescribed endomorphism ring

Daniel Herden, Héctor Gabriel Salazar Pedroza (2015)

Fundamenta Mathematicae

We will consider unital rings A with free additive group, and want to construct (in ZFC) for each natural number k a family of k -free A-modules G which are separable as abelian groups with special decompositions. Recall that an A-module G is k -free if every subset of size < k is contained in a free submodule (we will refine this in Definition 3.2); and it is separable as an abelian group if any finite subset of G is contained in a free direct summand of G. Despite the fact that such a module G is...

-representation and set-prolongations

Josef Mlček (1992)

Commentationes Mathematicae Universitatis Carolinae

By an -representation of a relation we mean its isomorphic embedding to 𝔼 = { x , y ; x y } . Some theorems on such a representation are presented. Especially, we prove a version of the well-known theorem on isomorphic representation of extensional and well-founded relations in 𝔼 , which holds in Zermelo-Fraenkel set theory. This our version is in Zermelo-Fraenkel set theory false. A general theorem on a set-prolongation is proved; it enables us to solve the task of the representation in question.

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