As Philip Scott says about Denis Higgs:

In category theory, he wrote an influential and beautiful long paper, "A category approach to Boolean valued set theory", which initiated many early students in topos theory in the 1970s to Omega-valued sets.

I wonder to know if there is a way to get access to the following paper by Higgs:

``A category approach to Boolean valued set theory''

Remarks. I am aware of some similar works, for example A category-theoretic approach to boolean-valued models of set theory or the book Sheaves in geometry and logic by Mac Lane and Moerdijk.

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    $\begingroup$ Afaik, a subsequent paper by him, Injectivity in the topos of complete Heyting algebra valued sets, contains most of the material from that preprint. $\endgroup$ Commented May 24, 2017 at 6:59
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    $\begingroup$ Why not just contact Phil Scott? He's alive and kicking. $\endgroup$ Commented May 24, 2017 at 7:41
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    $\begingroup$ @DavidHandelmanD I asked, but he doesn't have it. $\endgroup$ Commented May 24, 2017 at 14:00
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    $\begingroup$ It's probably worth asking the categories mailing list. I remember this paper being cited in Walters' "Sheaves on sites as Cauchy-complete categories". And with the number of citations it has (over 100 according to Google Scholar), somebody must have a copy. $\endgroup$
    – Tim Campion
    Commented May 24, 2017 at 23:49

1 Answer 1


Definitely not a answer, but too long for a comment, and just for completeness:

As pointed out by მამუკა ჯიბლაძე, Higgs writes in Injectivity in the Topos of Complete Heyting Algebra Valued Sets that this paper is related to the unpublished paper you are looking for (cited as [5] by Higgs):

An earlier version ( [5] ) of this paper was accepted for publication in the Canadian Mathematical Bulletin but for various reasons I discontinued the process of seeing it through into print. In addition to the present contents, [5] contained: a brief account of logic in $\mathcal L(\mathcal A)$; the Lawvere Tierney version (for $\mathcal L(\mathcal A)$) of the independence of the continuum hypothesis [14]; a sketch of a proof that $\mathcal L(\mathcal A)$ is equivalent to the category of sets within the universe $V^{\mathcal A}$ of $\mathcal A$-valued set theory; a mention of sheaves on an arbitrary site from the point of view of $\mathcal A$-valued sets; and some elementary remarks on boolean powers and ultrapowers in relation to $\mathcal L(\mathcal A)$.

[5] D. Higgs A category approach to boolean valued set theory, preprint, University of Waterloo (1973)

[14] M. Tierney, Sheaf theory and the continuum hypothesis, in Toposes, algebraic geometry and logic (F. W. Lawvere, éd.), 13-42, Lecture Notes in Mathematics 274 (SpringerVerlag, Berlin, Heidelberg, New York, 1972).

  • $\begingroup$ Thanks Jakob for the information. $\endgroup$ Commented Jun 13, 2020 at 3:26

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