# Scott-Solovay unpublished paper on Boolean valued models of set theory''

I have read some papers from 1970$^{th}$, and in some of them, the paper of Scott and Solovay on Boolean valued models of set theory'' is given as a main reference, with many references to the results from it. Unfortunately the paper never published.

Question 1. Does anyone know the historical reasons for not publishing the paper?

Of course I know there are some papers and books covering the topic, in particular:

1) Boolean-valued set theory and forcing by Richard Mansfield, John Dawson.

2) Set Theory: Boolean-Valued Models and Independence Proofs by John Bell.

The second reference gives some historical points about the creation of Boolean valued method. Though the above references are very good for learning the method, I am mainly interested in the original paper.

Question 2. Is there any typed or scanned version of the Scott-Solovay paper available? how can I find a version of the paper?

Of course, maybe the simplest answer is: send an email to one of the authors, and ask them about the paper. But I would rather first try the Mathoverflow.

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As it is stated in the answer below (and I was aware of it), the paper by Scott A proof of the independence of the continuum hypothesis'' presents some aspects of the theory. But it does not give answer to my questions.

• Solovay posted a couple of times on MO, maybe he can be made aware of this question. – Asaf Karagila Mar 11 '15 at 12:09
• Finally someone asked this! Thanks Mohammad! – shahram Mar 11 '15 at 12:12
• @shahram Thanks, I've been always interested in this paper, as it makes reading old papers easier, and it should be a fantastic paper. – Mohammad Golshani Mar 11 '15 at 12:22
• @ChristianRemling Also his work on the fine structure of $L[\mu],$ where $\mu$ is a normal measure on some measurable cardinal $\kappa.$ – Mohammad Golshani Mar 11 '15 at 15:23
• @MohammadGolshani, are there cited results from this paper that are not either not in standard textbooks like Jech and Kunen, or not commonly known "folklore" by forcing experts such as yourself? If so, can you write some examples? Thanks. – Monroe Eskew Mar 12 '15 at 4:11

Scott was editor of the Oxford logic guides and was involved in the preparation of Set Theory: Boolean-Valued Models and Independence Proofs (Oxford Logic Guides). He wrote a forward to it and in this passage he discusses the reasons it was not published:

"There are many references in the literature to the Scott–Solovay paper, which was to be published as an expanded version of the 1967 notes. This paper does not exist, and it is my own personal failing for not putting it together from the materials I had at hand. I discussed it several times with Robert Solovay, but we were not at the same institution and could not work very closely together. He drafted parts of certain sections, but he was working on so many papers at the same time that he did not have the opportunity to draft the whole paper. The present book essentially supplants the projected Scott–Solovay paper. Part of my own difficulty about writing the Scott–Solovay paper was the fantastic growth of the field and the speed with which it changed. During the winter of 1968–1969 I became profoundly discouraged because I felt unable to make any original contributions: any ideas I had were either wrong or already known. It is easy enough to say now that I should have been content to be a reporter and expositor, but, at the very moment when one is being left behind, things seem less pleasant. I put these remarks forward not as an excuse but simply as an explanation of why I could not complete what I set out to do."

• I wonder if this would have happened today, with emails, Skype cellphones and cloud sharing. – Asaf Karagila Mar 12 '15 at 22:09
• I am also interested to hear Prof. Solovay's reasons for not completing (and publishing) the work. – Mohammad Golshani Mar 14 '15 at 4:28

This is just a long comment and it is possible that nothing is new here for you.

"D. Scott, A proof of the independence of the continuum hypothesis", is an interesting prequel to the then "in preparation" Scott-Solovay paper (see reference 8 here) that never appeared.

It also appears that Scott lectured on this topic at the Fourteenth annual summer research institute on axiomatic set theory at UCLA in July-August 1967. The lecture notes were supposed to appear in volume two of these proceedings (see Shoenfield's article in volume one) but it never appeared in print.

• Well, at least one paper of Scott's appeared in this second volume: books.google.hu/… – Péter Komjáth Mar 12 '15 at 5:58
• When I was a grad. student in Oxford (75-78) there was a loose-leaf bound copy (not even a "photo" copy but some other kind) of Scott's lecture notes from the UCLA year on the shelves in the graduate room. We consulted them, but no doubt they are lost now. – Philip Welch Mar 12 '15 at 18:23