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Some Remarks on Indicatrices of Measurable Functions

Marcin Kysiak (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

Some Remarks on Tall Cardinals and Failures of GCH

Arthur W. Apter (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

We investigate two global GCH patterns which are consistent with the existence of a tall cardinal, and also present some related open questions.

Some remarks on universality properties of / c

Mikołaj Krupski, Witold Marciszewski (2012)

Colloquium Mathematicae

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 / c . 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 / c , but fails to embed isometrically....

Some results about compact logics

Paolo Lipparini (1982)

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

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.

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