In [his paper "Forcing in admissible sets"](http://download.springer.com/static/pdf/739/art%253A10.1007%252FBF01978554.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2FBF01978554&token2=exp=1482366949~acl=%2Fstatic%2Fpdf%2F739%2Fart%25253A10.1007%25252FBF01978554.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252FBF01978554*~hmac=a4941d7ffb820ad1d9150617d0dce1a80f3dff56215fcb008f211f166713fb67), 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 In unpublished lectures given at Novosibirsk State University in 1976-1977 on the theory of admissible sets, the author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.*



History of forcing over admissible sets
Forcing over admissible sets was first carried out by Jon Barwise in his 1967 Stanford dissertation. 


[This recent paper](https://www.dpmms.cam.ac.uk/~ardm/fifofields3.pdf) 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.


