Around 1974, Leo Harringto wrote an unpublished note entitled "The constructible reals can be anything", in which he proved that it is consistent that being $\Delta^1\_n$ is the same as being constructible.


Harrington proved his theorem using a version of almost disjoint coding of Jensen and Solovay. 



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> Is there any reference in which a proof of the above theorem is given which is similar to the Harrington's original proof. 
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**Remark.** There are proofs of Harrington's theorem by Kanovei, using different methods, see for example 


(1) Kanovei. The independence of some propositions of descriptive set theory
and second order arithmetic. Soviet Math. Dokl . 1975, 16, 4, pp. 937 – 940.


(2) Kanovei. On the nonemptiness of classes in axiomatic set theory. Math.
USSR Izv. 1978, 12, pp. 507 – 535.



Harrington's unpublished note "The constructible reals can be anything"
It seems the Harrington's preprint is here <http://logic-library.berkeley.edu/catalog/detail/2135> but to access it requires CalNet login. Maybe Harrington himself could help if you write to him: <http://math.berkeley.edu/~leo/index.html>


P.S. Prof. Harrington kindly sent me a scan of the preprint. It can be found here 
<http://www.inp.nsk.su/~silagadz/Harrington.pdf>


