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- W2317641818 abstract "Let LS denote the language of (right) S-sets over a monoid S and let ∑ S be a set of sentences in LS which axiomatises S-sets. A general result of model theory says that ∑ S has a model companion, denoted by TS , precisely when the class E of existentially closed S-sets is axiomatisable and in this case, TS axiomatises E . It is known that TS exists and is stable if and only if S is right coherent. In the study of stable first order theories, superstable and totally transcendental theories are of particular interest. We describe types over TS algebraically and use our result to confirm that TS is stable. We prove that TS is superstable if and only if S satisfies the maximal condition for right ideals. The situation for total transcendence is more complicated but a usable result is obtained for the case where U -rank coincides with Morley rank." @default.
- W2317641818 created "2016-06-24" @default.
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- W2317641818 date "2008-06-01" @default.
- W2317641818 modified "2023-09-25" @default.
- W2317641818 title "STABILITY OF THE THEORY OF EXISTENTIALLY CLOSED S-ACTS OVER A RIGHT COHERENT MONOID S" @default.
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- W2317641818 doi "https://doi.org/10.1142/9789812790019_0009" @default.
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