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Furthermore, one of the deepest results in model theory is Morley's theorem (whose proof is too difficult to be included here) which asserts that the four possibilities above are exhaustive, that is, if a theory in a countable language is -categorical for some gt 0, it is -categorical for all gt 0. This aspect of Basic Model Theory Stanford University plays a vital role in practical applications.

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Furthermore, from this central area, the following directions sprout model theory for languages extending the first-order ones, abstract model theory, applied model theory non-standard analysis, algebraic model theory, model theory of other special theories, recursive model theory, finite-model theory, classification theory. This aspect of Basic Model Theory Stanford University plays a vital role in practical applications.

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Furthermore, one of the deepest results in model theory is Morley's theorem (whose proof is too difficult to be included here) which asserts that the four possibilities above are exhaustive, that is, if a theory in a countable language is -categorical for some gt 0, it is -categorical for all gt 0. This aspect of Basic Model Theory Stanford University plays a vital role in practical applications.

Moreover, since the 1970s, the subject has been shaped decisively by Saharon Shelah 's stability theory. Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit to classical mathematics. This aspect of Basic Model Theory Stanford University plays a vital role in practical applications.

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It covers the logical, linguistic, psychological and information-theoretic parts of the cognitive sciences as well as math- ematical tools for them. The emphasis is on the theoretical and inter- disciplinary aspects of these areas. This aspect of Basic Model Theory Stanford University plays a vital role in practical applications.

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Moreover, one of the deepest results in model theory is Morley's theorem (whose proof is too difficult to be included here) which asserts that the four possibilities above are exhaustive, that is, if a theory in a countable language is -categorical for some gt 0, it is -categorical for all gt 0. This aspect of Basic Model Theory Stanford University plays a vital role in practical applications.

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