Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposing Baire class 1 functions into continuous functions   Let dec be the least cardinal kappa such that every function of first Baire
class can be decomposed into kappa continuous functions. Cichon, Morayne,
Pawlikowski and Solecki proved that cov(Meager) <= dec <= d and asked whether
these inequalities could, consistently, be strict. By cov(Meager) is meant the
least number of closed nowhere dense sets required to cover the real line and
by d is denoted the least cardinal of a dominating family in omega^omega.
Steprans showed that it is consistent that cov(Meager) not= dec. In this paper
we show that the second inequality can also be made strict. The model where dec
is different from d is the one obtained by adding omega_2 Miller - sometimes
known as super-perfect or rational-perfect - reals to a model of the Continuum
Hypothesis. It is somewhat surprising that the model used to establish the
consistency of the other inequality, cov(Meager) not= dec, is a slight
modification of the iteration of super-perfect forcing.

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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int