论文信息 - Dimension theory and forcing

Dimension theory and forcing

Abstract There is a proper Baire category preserving forcing which adds infinitely equal real but no Cohen real. This resolves a long-standing open problem of David Fremlin. The forcing has a natural description in terms of infinite-dimensional topology.

Jindřich Zapletal | J. Zapletal

[1] Szymon Zeberski,et al. Topologically invariant σ-ideals on the Hilbert cube , 2015 .

[2] D. Henderson. An Infinite-Dimensional Compactum with no Positive-Dimensional Compact Subsets-A Simpler Construction , 1967 .

[3] Haim Judah,et al. Set Theory: On the Structure of the Real Line , 1995 .

[4] Saharon Shelah,et al. Proper and Improper Forcing , 1998 .

[5] Piotr Zakrzewski,et al. On Borel mappings and σ-ideals generated by closed sets , 2012 .

[6] John J. Walsh,et al. Infinite dimensional compacta containing no n-dimensional (n≥1) subsets , 1979 .

[7] Jindrich Zapletal,et al. Forcing Properties of Ideals of Closed Sets , 2010, The Journal of Symbolic Logic.

[8] Alain Louveau,et al. Descriptive Set Theory and the Structure of Sets of Uniqueness , 1987 .

[9] A. Kechris. Classical descriptive set theory , 1987 .

[10] F. Stephan,et al. Set theory , 2018, Mathematical Statistics with Applications in R.