A note on standard systems and ultrafilters
Keyword(s):
AbstractLet (M, )⊨ ACA0 be such that , the collection of all unbounded sets in , admits a definable complete ultrafilter and let T be a theory extending first order arithmetic coded in such that M thinks T is consistent. We prove that there is an end-extension N ⊨ T of M such that the subsets of M coded in N are precisely those in . As a special case we get that any Scott set with a definable ultrafilter coding a consistent theory T extending first order arithmetic is the standard system of a recursively saturated model of T.
1993 ◽
Vol 65
(2)
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pp. 125-148
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2010 ◽
Vol 16
(3)
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pp. 345-358
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1991 ◽
Vol 37
(13-16)
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pp. 207-216
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2016 ◽
Vol 10
(1)
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pp. 187-202
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