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We define a $\sigma$-centered notion of forcing that forces the existence ofa Boolean algebra with the Grothendieck property and without the Nikodymproperty. In particular the existence of such an algebra is consistent with thenegation of the continuum hypothesis. The algebra we construct consists ofBorel subsets of the Cantor set and has cardinality $\omega_1$. We also showhow to apply our method to streamline Talagrand's construction of such analgebra under the continuum hypothesis.

Epic math battle of history: Grothendieck vs Nikodym