Ha ha ha ha!! He just fucking say it Hahahah... He actually called her "his girlfriend" xD
Even if a translation bleep its still hylarious, calling a slave with no free will you girlfriend/boyfriend is like saying that your dog loves you because of who you are xD
Seriously, whats with the japanese people portraid in this kind of stories?? Aren't the authors aware that slavery is a bad thing?? Even if they want to use the argument that "It's a different world, so there are different rules" that doesn't mean that the MC doesn't have "modern" world values. I get the necesity to get a guide to help you understand the whos and wheres, but come on impossing yourself phisically over someone you bought can't be really called sincere affection, no matter how "pure" said feelings are...
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On the other hand, can't argue the art its pretty good and the story seems enjoyable, bleeps and inconsistenscies aside.