Connectedness of the theory of non-surjective injections
نویسنده
چکیده
It is shown that the first-order theory T of a non-surjective injection (of the universe into itself) is connected. By a criterion for connectedness, due to J. Mycielski, one reduces this result to the following theorem: If A, B are any structures and ε is a definable equivalence relation on their disjoint product A ×̇B such that (A ×̇B)/ε is a model of T, then either A has the property that for some finite structure S and a definable equivalence relation ' on S ×̇ A, (S ×̇ A)/' is a model of T, or the analogous property
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