Fields with few types
Keyword(s):
AbstractAccording to Belegradek, a first order structure is weakly small if there are countably many 1-types over any of its finite subset. We show the following results. A field extension of finite degree of an infinite weakly small field has no Artin-Schreier extension. A weakly small field of characteristic 2 is finite or algebraically closed. A weakly small division ring of positive characteristic is locally finite dimensional over its centre. A weakly small division ring of characteristic 2 is a field.
1995 ◽
Vol 38
(1)
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pp. 63-76
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2019 ◽
Vol 28
(14)
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pp. 1944006
2010 ◽
Vol 06
(07)
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pp. 1541-1564
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1999 ◽
Vol 51
(3)
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pp. 488-505
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