The prefrontal cortex (PFC) plays a crucial role in cognitive control and higher mental functions by maintaining working memory representations of currently relevant information, thereby inducing a mindset that facilitates the processing of such information. Using fMRI, we examined how the human PFC implements mindsets for information at varying levels of abstraction. Subjects solved anagrams grouped into three kinds of blocks (concrete, moderately abstract, and highly abstract) according to the degree of abstraction of their solutions. Mindsets were induced by cuing subjects at the beginning of every block as to the degree of abstraction of solutions they should look for. Different levels of abstraction were matched for accuracy and reaction time, allowing us to examine the effects of varying abstraction in the absence of variations in cognitive complexity. Mindsets for concrete, moderately abstract, and highly abstract information were associated with stronger relative recruitment of ventrolateral, dorsolateral, and rostrolateral PFC regions, respectively, suggesting a functional topography whereby increasingly anterior regions are preferentially associated with representations of increasing abstraction. Rather than being a structural property of the neurons in different prefrontal subregions, this relative specialization may reflect one of the principles according to which lateral PFC adaptively codes and organizes task-relevant information.