Bourbaki theory of isomorphism, examples of untransportable formulas - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T10:55:16Z http://mathoverflow.net/feeds/question/28744 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/28744/bourbaki-theory-of-isomorphism-examples-of-untransportable-formulas Bourbaki theory of isomorphism, examples of untransportable formulas Victor Makarov 2010-06-19T12:02:41Z 2010-06-22T14:00:08Z <p>In their book "Theory of sets" Bourbaki suggested a general theory of isomorphism.</p> <p>(See also <a href="http://www.tau.ac.il/~corry/publications/articles/pdf/bourbaki-structures.pdf" rel="nofollow">http://www.tau.ac.il/~corry/publications/articles/pdf/bourbaki-structures.pdf</a> )</p> <p>The example of an untransportable relation (i.e. formula) in the book involves 2 principal base sets.</p> <p>Are there examples of untrasportable formulas when we allow only one principal base set?</p> http://mathoverflow.net/questions/28744/bourbaki-theory-of-isomorphism-examples-of-untransportable-formulas/28989#28989 Answer by Victor Makarov for Bourbaki theory of isomorphism, examples of untransportable formulas Victor Makarov 2010-06-21T20:17:34Z 2010-06-22T14:00:08Z <p>An example of untrasportable sentence, when there is only one principal base set X, may be the following one: </p> <p>All elements of the set X are finite sets,</p> <p>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.</p> <p>A simpler example is "the set X contains the empty set". </p> <p>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. </p>