How long until I can claim this cat?

We found a stray cat stuck in our tree about 40 feet up, we had an arborist come get him down after 3 days of trying to coax him down. We've had him in our home for a week now and no one has claimed him or posted anything looking for him. I posted on various sites about him and no response. I took him to the... show more We found a stray cat stuck in our tree about 40 feet up, we had an arborist come get him down after 3 days of trying to coax him down. We've had him in our home for a week now and no one has claimed him or posted anything looking for him. I posted on various sites about him and no response. I took him to the vet and he isn't chipped. He isn't fixed or declawed either, we're becoming attached to this cat and he's so sweet with the 2 year old and our cats (2) and dog. How long do we have to wait for someone to claim him before we can keep him as our own?
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