Q1: Except for those quotes, is there any tangible trace of such a proof obtained by Gödel?

Gödel commented on his independence results in a letter of 1967 to W. Rautenberg. In his reply (in German, translated here), Gödel confirmed what Church had stated:

In reply to your inquiry I would like to refer to the presentation of the facts that Professor Alonzo Church gave in his lecture at the last International Congress of Mathematicians. Mostowski's assertion _{[that Gödel, about 1940, had obtained most of Cohen's independence results]}is incorrect insofar as I was merely in possession of certain partial results, namely, of proofs for the independence of the axiom of constructibility and of the axiom of choice in type theory. Because of my highly incomplete records from that time, _{[entries in volumes 1 and 15 of his Arbeitshefte from Summer 1942]} I can only reconstruct the first of these two proofs without difficulty. My method had a very close connection with that recently developed by Dana Scott and had less connection with Cohen's method. I never obtained a proof for the independence of the continuum hypothesis from the axiom of choice, and I found it very doubtful that the method that I used would lead to such a result.

Q1: Except for those quotes, is there any tangible trace of such a proof obtained by Gödel?

Gödel commented on his independence results in a letter dated June 30, 1967 to W. Rautenberg. In his reply (in German, translated here), Gödel confirmed what Church had stated:

In reply to your inquiry I would like to refer to the presentation of the facts that Professor Alonzo Church gave in his lecture at the last International Congress of Mathematicians. Mostowski's assertion _{[that Gödel, about 1940, had obtained most of Cohen's independence results]}is incorrect insofar as I was merely in possession of certain partial results, namely, of proofs for the independence of the axiom of constructibility and of the axiom of choice in type theory. Because of my highly incomplete records from that time, _{[entries in volumes 1 and 15 of his Arbeitshefte from Summer 1942]} I can only reconstruct the first of these two proofs without difficulty. My method had a very close connection with that recently developed by Dana Scott and had less connection with Cohen's method. I never obtained a proof for the independence of the continuum hypothesis from the axiom of choice, and I found it very doubtful that the method that I used would lead to such a result.

Q1: Except for those quotes, is there any tangible trace of such a proof obtained by Gödel?

Gödel commented on his independence results in a letter of 1967 to W. Rautenberg. In his reply (in German), Gödel confirmed what Church had stated:

In reply to your inquiry I would like to refer to the presentation of the facts that Professor Alonzo Church gave in his lecture at the last International Congress of Mathematicians. Mostowski's assertion _{[that Gödel, about 1940, had obtained most of Cohen's independence results]}is incorrect insofar as I was merely in possession of certain partial results, namely, of proofs for the independence of the axiom of constructibility and of the axiom of choice in type theory. Because of my highly incomplete records from that time, _{[entries in volumes 1 and 15 of his Arbeitshefte from Summer 1942]} I can only reconstruct the first of these two proofs without difficulty. My method had a very close connection with that recently developed by Dana Scott and had less connection with Cohen's method. I never obtained a proof for the independence of the continuum hypothesis from the axiom of choice, and I found it very doubtful that the method that I used would lead to such a result.

[source]

Q1: Except for those quotes, is there any tangible trace of such a proof obtained by Gödel?

Gödel commented on his independence results in a letter of 1967 to W. Rautenberg. In his reply (in German, translated here), Gödel confirmed what Church had stated:

In reply to your inquiry I would like to refer to the presentation of the facts that Professor Alonzo Church gave in his lecture at the last International Congress of Mathematicians. Mostowski's assertion _{[that Gödel, about 1940, had obtained most of Cohen's independence results]}is incorrect insofar as I was merely in possession of certain partial results, namely, of proofs for the independence of the axiom of constructibility and of the axiom of choice in type theory. Because of my highly incomplete records from that time, _{[entries in volumes 1 and 15 of his Arbeitshefte from Summer 1942]} I can only reconstruct the first of these two proofs without difficulty. My method had a very close connection with that recently developed by Dana Scott and had less connection with Cohen's method. I never obtained a proof for the independence of the continuum hypothesis from the axiom of choice, and I found it very doubtful that the method that I used would lead to such a result.