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

Abstract

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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 ω ω is ℵ 2 . The model used in the one obtained by adding ω 2 Miller reals to a model of the Continuum Hypothesis.

How to cite

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Shelah, 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

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  1. [1] J. Cichoń, M. Morayne, J. Pawlikowski, and S. Solecki, Decomposing Baire functions, J. Symbolic Logic 56 (1991), 1273-1283. Zbl0742.04003
  2. [2] M. Groszek, Combinatorics on ideals and forcing with trees, ibid. 52 (1987), 582-593. Zbl0646.03048
  3. [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. [4] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, Berlin, 1982. 
  5. [5] J. Steprāns, A very discontinuous Borel function, J. Symbolic Logic 58 (1993), 1268-1283. Zbl0805.03036

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