E
*-Stable Theories |
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Authors: | E A Palyutin |
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Institution: | (1) Akademika Koptyuga Prospekt, 4, Institute of Mathematics SB RAS, Novosibirsk, 630090 |
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Abstract: | S. Shelah proved that stability of a theory is equivalent to definability of every complete type of that theory. T. Mustafin introduced the concept of being T
*-stable, generalizing the notion of being stable. However, T
*-stability does not necessitate definability of types. The key result of the present article is proving the definability of types for E
*-stable theories. This concept differs from that of being T
*-stable by adding the condition of being continuous. As a consequence we arrive at the definability of types over any P-sets in P-stable theories, which previously was established by T. Nurmagambetov and B. Poizat for types over P-models. |
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Keywords: | E
*-stable theory definability of types |
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