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- W2009755770 abstract "For an ultrafilter , consider the ultrapower N N / . 〈 a n 〉/ is in the top sky of N N / if there exists a sequence 〈 b n 〉 ∈ N N such that and In [M2] we showed, assuming the Continuum Hypothesis, that there are exactly 10 c/p 's (where c is the ring of real convergent sequences and p is a prime ideal of c ). To get the lower bound we showed that there will be at least 10 c/p 's in any model of ZFC where there exist both of the following kinds of ultrafilter: (i) nonprincipal P -points, (ii) non- P -points such that when the top sky is removed from N N / , the remaining model has countable cofinality. In [M2] we showed that the Continuum Hypothesis implies the existence of the ultrafilter in (ii). In this paper we show that its existence is implied by an axiom weaker than the Continuum Hypothesis, in fact weaker than Martin's Axiom, namely, (*) If is a subset of N N such that for any f : N → N there exists g ∈ such that g ( n ) > f ( n ) for all n , then ∣ ∣ = ." @default.
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- W2009755770 date "1993-12-01" @default.
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- W2009755770 title "An existence theorem for a special ultrafilter when 𝔡 = 𝔠 " @default.
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- W2009755770 doi "https://doi.org/10.2307/2275148" @default.
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