TITLE: History of forcing over admissible sets
QUESTION [6 upvotes]: In his paper "Forcing in admissible sets", Ershov writes

In unpublished lectures given at Novosibirsk State University in 1976-1977 on the theory of admissible sets, the author
  showed that it is possible to use forcing to construct admissible sets. The possibility of using forcing in the theory of admissible sets was suggested in a number of publications, but a precise exposition of this method was never published. The present paper, which is based on notes from the lectures mentioned above, attempts to fill this gap. 

I'm curious about the extent of the "suggestions" that Ershov mentions. Specifically: would it be fair to credit Ershov solely with the result that set forcing preserves admissibility, or should that be Ershov/folklore (or something else)?
Context: I'm writing a paper where I use this result, and would like to attribute it appropriately.

REPLY [7 votes]: Forcing over admissible sets was first carried out by Jon Barwise in his 1967 Stanford dissertation. 
This recent paper of Mathias (it appeared in Fundamenta Mathamaticae in 2015) develops forcing over set theories that are weaker than KP. It also has a nice historical section (page 31) on the topic of forcing over weak set theories.