MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

In their book "Theory of sets" Bourbaki suggested a general theory of isomorphism.

(See also )

The example of an untransportable relation (i.e. formula) in the book involves 2 principal base sets.

Are there examples of untrasportable formulas when we allow only one principal base set?

share|cite|improve this question
Very few people here are familiar with Bourbaki's set theory. You should probably state the definitions here as well. – Harry Gindi Jun 19 '10 at 12:14
A reference is added in the question. – Victor Makarov Jun 22 '10 at 13:44
up vote 1 down vote accepted

An example of untrasportable sentence, when there is only one principal base set X, may be the following one:

All elements of the set X are finite sets,

Because, by definition, the truth value of a transportable sentence must be preserved under all bijections from the set X. Obviously, there exists a bijection from X to a set Y, where not all elements of Y are finite sets.

A simpler example is "the set X contains the empty set".

There is a paper "Sentences of type theory: the only sentences preserved under isomorphisms" by Victoria Marshall and Rolando Chuaqui - see The Journal of symbolic Logic, vol 56, #3, Sep 1991.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.