## Journal of Symbolic Logic

### Powers of the Ideal of Lebesgue Measure Zero Sets

Maxim R. Burke

#### Abstract

We investigate the cofinality of the partial order $\mathscr{N}^\kappa$ of functions from a regular cardinal $\kappa$ into the ideal $\mathscr{N}$ of Lebesgue measure zero subsets of $\mathbf{R}$. We show that when add$(\mathscr{N}) = \kappa$ and the covering lemma holds with respect to an inner model of GCH, then $\mathrm{cf}(\mathscr{N}^\kappa) = \max \{\mathrm{cf}(\kappa^\kappa), \mathrm{cf}(\lbrack \mathrm{cf}(\mathscr{N})\rbrack^\kappa)\}$. We also give an example to show that the covering assumption cannot be removed.

#### Article information

Source
J. Symbolic Logic, Volume 56, Issue 1 (1991), 103-107.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183743553

Mathematical Reviews number (MathSciNet)
MR1131732

Zentralblatt MATH identifier
0729.03023

JSTOR