There are some forms of set theory in which there are restrictions on the forms of comprehension allowed, and as a result there is a set of all sets. Quine's New Foundations is one of these. It has a simple restriction on the forms of predicates allowed in comprehensions. Put simply this is that you can assign (integer) levels to the variables in the formula so that x e y only occurs when y is at the level immediately above x. This means that in models of this set theory there is also an internal category of all sets. best Edmund On 4 Sep 2013, at 10:23, Andrej Bauer wrote:
Chatting at a conference, the question came up why there is no (non-trivial) category which is "internal to itself" (interpret this in some sensible sense). And over coffee we thought this must be well known, but not to us. Can somene shed some light on the matter?
With kind regards,
Andrej
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