Hope someone can help me.
I've found my granddad in the U.S. Naturalization Record Indexes, 1791-1992 (Indexed in World Archives Project). Index to Naturalization Records of the U.S. District for the Eastern District of Tennessee at Chattanooga
As far as I can make out the index states his name, Valdemar Pedersen (they write Pederson, but it's him) and
"Book 7 - pet. no. 15 vim"
Dec. 7. 1918
How do I go about finding the petitions and/or declarations?
(I've also found him on a passenger list coming from Denmark, and as drafted in WWI 1918 and also a passport request.)