We give a proof of GĂ¶del's first incompleteness theorem based on Berry's paradox, and from it we also derive the second incompleteness theorem model-theoretically.

@article{Kikuchi1994,
title = {A Note on Boolos' Proof of the Incompleteness Theorem},
author = {Kikuchi, Makoto},
url = {http://doi.wiley.com/10.1002/malq.19940400409},
urldate = {2010-09-03},
abstract = {We give a proof of G{\"{o}}del's first incompleteness theorem based on Berry's paradox, and from it we also derive the second incompleteness theorem model-theoretically.},
comment = {},
journal = {Mathematical Logic Quarterly},
number = 4,
pages = {528--532},
volume = 40,
year = 1994,
collections = {About proof}
}