Cattell, together with John Horn, later expanded the G"f"-G"c" model to include a number of other broad abilities, such as G"q" (quantitative reasoning) and G"v" (visual-spatial reasoning). While all the broad ability factors in the extended G"f"-G"c" model are positively correlated and thus would enable the extraction of a higher order "g" factor, Cattell and Horn maintained that it would be erroneous to posit that a general factor underlies these broad abilities. They argued that "g" factors computed from different test batteries are not invariant and would give different values of "g", and that the correlations among tests arise because it is difficult to test just one ability at a time.