It is shown to be consistent that every function of first Baire class can be decomposed into continuous functions yet the least cardinal of a dominating family in is . The model used in the one obtained by adding Miller reals to a model of the Continuum Hypothesis.
@article{bwmeta1.element.bwnjournal-article-fmv145i2p171bwm, author = {Saharon Shelah and Juris Steprans}, title = {Decomposing Baire class 1 functions into continuous functions}, journal = {Fundamenta Mathematicae}, volume = {144}, year = {1994}, pages = {171-180}, zbl = {0821.03022}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv145i2p171bwm} }
Shelah, Saharon; Steprans, Juris. Decomposing Baire class 1 functions into continuous functions. Fundamenta Mathematicae, Tome 144 (1994) pp. 171-180. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv145i2p171bwm/
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