Some remarks on embeddings of Boolean algebras and topological spaces
We show that for a wide class of σ-algebras 𝓐, indicatrices of 𝓐-measurable functions admit the same characterization as indicatrices of Lebesgue-measurable functions. In particular, this applies to functions measurable in the sense of Marczewski.
We investigate two global GCH patterns which are consistent with the existence of a tall cardinal, and also present some related open questions.
We prove that if is not a Kunen cardinal, then there is a uniform Eberlein compact space K such that the Banach space C(K) does not embed isometrically into . We prove a similar result for isomorphic embeddings. Our arguments are minor modifications of the proofs of analogous results for Corson compacta obtained by S. Todorčević. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into , but fails to embed isometrically....
Nell'ambito della Teoria dei Modelli Astratta è possibile dimostrare che una logica compatta L è univocamente determinata dalla sua relazione di L-elementare equivalenza (Teorema 1). Si enunciano poi alcuni risultati sulle logiche massime correlate a certe relazioni di equivalenza e sulle logiche compatte generate da qualche sistema di Fraissé-Ehrenfeucht.