科研之友
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摘要
In this paper, we give an example of a complete computable infinitary theory T with countable models and , where is a proper computable infinitary extension of and T has no uncountable model. In fact, and are (up to isomorphism) the only models of T. Moreover, for all computable ordinals alpha, the computable part of T is hyperarithmetical. It follows from a theorem of Gregory (JSL 38:460-470, 1972; Not Am Math Soc 17:967-968, 1970) that if T is a I (1) (1) set of computable infinitary sentences and T has a pair of models and , where is a proper computable infinitary extension of , then T would have an uncountable model.
- 出版日期2013-5
