Cut $\mathbb{N^{+}}$

Can we divide $\mathbb{N^{+}}$ into two sets $A$ and $B$ $\big($ i.e. $A\cap B=\emptyset, A\cup B =\mathbb{N^{+}}\big)$ such that

1. no three distinct elements in $A$ can form an arithmetic progression;
2. there does not exist a non-constant, infinite arithmetic progression made up of elements in $B?$