# Decomposing Baire class 1 functions into continuous functions

Saharon Shelah; Juris Steprans

Fundamenta Mathematicae (1994)

- Volume: 145, Issue: 2, page 171-180
- ISSN: 0016-2736

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topShelah, Saharon, and Steprans, Juris. "Decomposing Baire class 1 functions into continuous functions." Fundamenta Mathematicae 145.2 (1994): 171-180. <http://eudml.org/doc/212041>.

@article{Shelah1994,

abstract = {It is shown to be consistent that every function of first Baire class can be decomposed into $ℵ_1$ continuous functions yet the least cardinal of a dominating family in $^ωω$ is $ℵ_2$. The model used in the one obtained by adding $ω_2$ Miller reals to a model of the Continuum Hypothesis.},

author = {Shelah, Saharon, Steprans, Juris},

journal = {Fundamenta Mathematicae},

keywords = {Baire class 1 function; superperfect forcing},

language = {eng},

number = {2},

pages = {171-180},

title = {Decomposing Baire class 1 functions into continuous functions},

url = {http://eudml.org/doc/212041},

volume = {145},

year = {1994},

}

TY - JOUR

AU - Shelah, Saharon

AU - Steprans, Juris

TI - Decomposing Baire class 1 functions into continuous functions

JO - Fundamenta Mathematicae

PY - 1994

VL - 145

IS - 2

SP - 171

EP - 180

AB - It is shown to be consistent that every function of first Baire class can be decomposed into $ℵ_1$ continuous functions yet the least cardinal of a dominating family in $^ωω$ is $ℵ_2$. The model used in the one obtained by adding $ω_2$ Miller reals to a model of the Continuum Hypothesis.

LA - eng

KW - Baire class 1 function; superperfect forcing

UR - http://eudml.org/doc/212041

ER -

## References

top- [1] J. Cichoń, M. Morayne, J. Pawlikowski, and S. Solecki, Decomposing Baire functions, J. Symbolic Logic 56 (1991), 1273-1283. Zbl0742.04003
- [2] M. Groszek, Combinatorics on ideals and forcing with trees, ibid. 52 (1987), 582-593. Zbl0646.03048
- [3] A. Miller, Rational perfect set forcing, in: Axiomatic Set Theory, D. A. Martin, J. Baumgartner and S. Shelah (eds.), Contemp. Math. 31, Amer. Math. Soc., Providence, R.I., 1984, 143-159.
- [4] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, Berlin, 1982.
- [5] J. Steprāns, A very discontinuous Borel function, J. Symbolic Logic 58 (1993), 1268-1283. Zbl0805.03036

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