Decomposing Baire class 1 functions into continuous functions

• Autorzy: Saharon Shelah , Juris Steprans
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994
• Tom: 145
• Numer: 2
• Strony: 171-180

Daty

wydano

1994

otrzymano

1993-07-16

poprawiono

1994-02-24

Twórcy

autor

Saharon Shelah

• Institute of Mathematics, Hebrew University, Jerusalem, Givat Ram, Israel
• Department of Mathematics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3

autor

Juris Steprans

• Department of Mathematics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3

Bibliografia

• [1] J. Cichoń, M. Morayne, J. Pawlikowski, and S. Solecki, Decomposing Baire functions, J. Symbolic Logic 56 (1991), 1273-1283.
• [2] M. Groszek, Combinatorics on ideals and forcing with trees, ibid. 52 (1987), 582-593.
• [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.