12000 miles on car dealership says my oil is sluggish

Your first service, per Hyundai, for changing oil and filter should be done at 3,000 miles indeed...or at 6 months, whichever comes first. Additional oil and filter changes from there should be done at the minimum every 6 months or 5,000 miles, whichever occurs first. These are listed as "service warranty requirements" in the service manual. I would work with service management and with Hyundai for assistance if there is an issue.

Why did head gasket replacement come up as a necessity? .. What remedy did the dealer suggest?