Abstract
We present an analysis on the existentially closed (e.c.) structures for some theoryT in a rather complete categorical setting. The central notion of the skeleton ofT is defined. We formulate conditions on the skeleton which limit the number of e.c. structures forT, thereby ensuring the existence of a model-companion ofT. A new (purely categorical) proof of the uniqueness of the atomic structure is given for theories having the joint-embedding-property (JEP).
As an application it is shown that a finitely generated universal Horn class possesses a model-companion — a resuilt that was proved earlier by a different method.
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References
Bürger, G.,Modellbegleiter einiger Varietäten. Diplomarbeit Freiburg, 1985.
Burris, S andSankappanavar, H. P.,A Course in Universal Algebra. Springer-Verlag, New York, 1981.
Burris, S. andWerner, H.,Sheaf constructions and their elementary properties. Trans. AMS248 (1979), 269–309.
MacIntyre, A.,Model-completeness, in:Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977.
Maier, B.,On countable locally described structures. Ann. Pure Appl. Log.35 (1987), 205–246.
Schubert, H.,Kategorien I, II. Springer-Verlag, New York, 1970.
Simmons, H.,Large and small e.c. structures. JSL41, 379–390.
Weispfenning, V.,A note on ℵ 0-categorical model-companions. Arch. math. Logik19 (1978), 23–29.
Kunen K.,Set Theory. North-Holland, Amsterdam, 1980.
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Bürger, G. Finding model-companions via the skeleton. Algebra Universalis 27, 230–242 (1990). https://doi.org/10.1007/BF01182455
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DOI: https://doi.org/10.1007/BF01182455