$Omega$上非主算术超滤存在性的.pdf

492 Vol.49, No.2 20063 ACTA MATHEMATICA SINICA, Chinese Series Mar., 2006 : 0583-1431(2006)01-0283-06 : A ω 230026 E-mail: ftwang@ustc.edu.cn p ∈ βω −ω Np = {f (p ) : f ∈ ω ω } ⊃ N. () . , Æ. , Martin MAcountable Q: (Q) B ⊂ P (ω ) sfip () |B | 2ω , Q q ⊃ B. Q ω . Q ; ; MR(2000) 03E35, 03E65, 54D80 O144.3, O189.11 A Theorem on the Existence of Nonprincipal Arithmetical Ultrafilters on ω Fang Ting WANG Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China E-mail: ftwang@ustc.edu.cn Abstract Each nonprincipal arithmetical ultrafilter p ∈ βω − ω is associated with a simple arithmetical model N ω p = {f (p ) : f ∈ ω } ⊃ N, and a positive real number is just an equivalence class of finite fractions made by arithmetical ultrafilters (instead of natural numbers), just like the ancient Greek’s idea. It is well known that MAcountable implies the statement (Q): (Q) If B ⊂ P (ω ) has the sfip (strong finite intersection property) and |B | 2ω , then there is a Q-point q ⊃ B. In this paper we will prove that the statement (Q) implies our Hypothesis: There exist nonprincipal arithmetical ultrafilters on ω . Keywords Q-point; arithmetical ultrafilter; arithmetical model MR(2000) Subject Classification 03E35, 03E65, 54D80 Chinese Library Classification O144.3, O189.11 1 ˇ βω ( ω Stone-C