It is known that in ZF, the axiom of choice and the antichain principle (every partially ordered set has a maximal antichain) are equivalent. However, in ZF-Foundation, while AC still implies the antichain (maximality) principle (which I'll call AMP), the converse is not necessarily true. This also implies that the proof that AMP => AC in ZF is not "trivial".
Are there known choice principles which are implied by AMP in ZF-Foundation, something like "AMP => BPI" for example. Or "AMP => DC", etc ...
Also, is there a choice principle weaker than AC which is known to not be implied by AMP (In ZF - Foundation)?