certain types of polynomials in the neural ideal gives information about the relationships among receptive fields [@Neural_Rings]. For example, consider two neurons that never fire at the same time. The corresponding neural code might be $C =  \{ [1,0], [0,1], [0,0] \}$, and this code is associated with the ideal $J_C = \langle x_1x_2 \rangle$. As we will see, the fact that $x_1x_2 \in J_C$ implies that the receptive fields of neuron 1 and neuron 2 do not overlap. So if $U_1$ is the receptive field of neuron 1 and $U_2$ is the receptive field of neuron 2, $U_1 \cap U_2 = \emptyset$ is a receptive field relation that can be read off from $J_C$; it is known as a Type 1 relation. Also, it can be shown that the presence of a Type 1 relation implies that $x_1x_2 \in J_C$. Thus, the relationship between $J_C$ and the Type 1 relation is if-and-only-if.

Curto et al. found three receptive field relationships, known as the Type 1-3 relationships, that can be read off from the neural ideal. The three if-and-only-if statements relating the Type 1-3 relationships to the polynomials in the neural ideal are also loosely called the Type 1-3 relations. 