It was pointed out to me that Leon Henkin's PhD thesis, "The Completeness Of Formal Systems" is not digitized or easily available, and the UC libraries had a copy.

So I have scanned it and posted it to archive.org: https://archive.org/details/the-completeness-of-formal-systems

Because it is old and faded, and in parts handwritten, the OCR isn't very accurate.

According to everything I have read it should be in public domain as it lacks a copyright notice and was published in 1947. So hopefully I don't go to jail.