Journal of Symbolic Logic

Powers of the Ideal of Lebesgue Measure Zero Sets

Maxim R. Burke

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.


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

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

First available in Project Euclid: 6 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
Secondary: 03E10: Ordinal and cardinal numbers 03E35: Consistency and independence results


Burke, Maxim R. Powers of the Ideal of Lebesgue Measure Zero Sets. J. Symbolic Logic 56 (1991), no. 1, 103--107.

Export citation