Some unpublished Reclaw theorems and their applications to Baire-star-one functions

Authors: TOMASZ NATKANIEC, WALDEMAR SIEG

Abstract: Lunina's 7-tuples $\langle E^1,\ldots, E^7\rangle$ of sets of pointwise convergence, divergence to $\infty$, divergence to $-\infty$, etc. for sequences of Baire-star-one functions are cha\-racterized. Generalization on ideal convergence of such sequences is discussed. Limits and ideal limits of sequences of Baire-star-one functions are considered in the last part of the article.

Keywords: Pointwise convergence, ideal convergence, $F_\sigma$-ideal, $\cI^\star$-universal set, $\omega$-diagonalizability, Lunina 7-tuples, Baire-one-star functions

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