Both humans and transformer language models are able to learn language without explicit structural supervision. What inductive learning biases make this learning possible? In this study, we examine the effect of different inductive learning biases by predisposing language models with structural biases through pretraining on artificial structured data, and then evaluating by fine-tuning on English. Our experimental setup gives us the ability to actively control the inductive bias of language models. With our experiments, we investigate the comparative success of three types of inductive bias: 1) an inductive bias for recursive, hierarchical processing 2) an inductive bias for unrestricted token-token dependencies that can't be modeled by context-free grammars, and 3) an inductive bias for a Zipfian power-law vocabulary distribution. We show that complex token-token interactions form the best inductive biases, and that this is strongest in the non-context-free case. We also show that a Zipfian vocabulary distribution forms a good inductive bias independently from grammatical structure. Our study leverages the capabilities of transformer models to run controlled language learning experiments that are not possible to run in humans, and surfaces hypotheses about the structures that facilitate language learning in both humans and machines.