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Model Theory of Epimorphisms

Published online by Cambridge University Press:  20 November 2018

Paul D. Bacsich
Paul D. Bacsich*
Affiliation:
Mathematical Institute, Oxford
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Given a first-order theory T, welet be the category of models of T and homomorphisms between them. We shall show that a morphism A→B of is an epimorphism if and only if every element of B is definable from elements of A in a certain precise manner (see Theorem 1), and from this derive the best possible Cowell- power Theorem for .

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 471 - 477
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Aronszajn, N. and Panitchpakdi, P., Extension of uniformly continuous functions and hyperconvex metric spaces, Pac. J. Math. 6 (1956), 405-439.Google Scholar
2. Bacsich, P., Injectivity in Model Theory, Colloq. Math. 25 (1972), 165-176.Google Scholar
3. Bacsich, P., An epi-reflector for universal theories, Canad. Math. Bull. 16(2) (1973), 167-171.Google Scholar
4. Bell, J. and Slomson, A., Models and ultraproducts, North-Holland, Amsterdam, 1969.Google Scholar
5. Day, A., Injectivity in equational classes of algebras, Canad. J. Math. 24 (1972), 209-220.Google Scholar
6. Freyd, P., Abelian categories, Harper & Row, New York, 1964.Google Scholar
7. Grätzer, G., Universal Algebra, Van Nostrand, Princeton, 1968.Google Scholar
8. Isbell, J., Epimorphisms and dominions, in: Proceedings of the Conference on Categorical Algebra, La Jolla 1965, Springer-Verlag, Berlin, 1967.Google Scholar
9. Kelly, G., Monomorphisms, epimorphisms, and pull-backs, J. Austral. Math. Soc. 9 (1969), 124-142.Google Scholar
10. Kreisel, G., Model-theoretic invariants: applications to recursive and hyper arithmetic operations, in: The Theory of Models, North-Holland, Amsterdam, 1965.Google Scholar
11. Lawvere, W., Some algebraic problems in the context of functorial semantics of algebraic theories, in: Lecture Notes in Mathematics 61, Springer-Verlag, Berlin, 1968.Google Scholar
12. McKinsey, J., The decision problem for some classes of sentences without quantifiers, J. Symb. Logic 8 (1943), 61-76.Google Scholar
13. Scott, W., Algebraically closed groups, Proc. Amer. Math. Soc. 2 (1951), 118-121.Google Scholar
14. Storrer, H., Epimorphismen Von Kommutativen Ringen, Comment. Math. Helv. 43 (1968), 378-401.Google Scholar
15. Taylor, W., Residually small varieties, Algebra Universalis 2 (1972), 33-53.Google Scholar
16. Tarski, A., Mostowski, A., Robinson, A., Undecidable theories, North-Holland, Amsterdam, 1953.Google Scholar