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Si dimostra che la conoscenza delle algebre di Boole dei definibili di modelli di cardinità di una teoria elementare è sufficiente per decidere il suo tipo di stabilità.
Ogni logica genera canonicamente la -equivalenza e la -immersione proprio come la logica del primo ordine genera l’equivalenza elementare e l’immersione elementare . Astraendo da , 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 (). Caratterizziamo algebricamente quelle...
We will consider unital rings A with free additive group, and want to construct (in ZFC) for each natural number k a family of -free A-modules G which are separable as abelian groups with special decompositions. Recall that an A-module G is -free if every subset of size 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...
By an -representation of a relation we mean its isomorphic embedding to . 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 , 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.
We prove that MAX-3SAT can be approximated in polynomial time within a factor 1.0957 on random instances.
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