1998 Fiscal Year Final Research Report Summary
Properties of ideals on the real line
| Project/Area Number |
09640288
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
KAMO Shizuo College of Integrated Arts and Sciences, Osaka Prefecture University, Professor, 総合科学部, 教授 (30128764)
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| Project Period (FY) |
1997 – 1998
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| Keywords | cardinal invariant / forcing / predictor / evasion numbers |
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| Research Abstract |
We denote by omega the set of natural numbers. Let 2 <less than or equal> K <less than or equal>omega. A function from K^<<omega> to K is called a K-predictor. We say that a K-predictor PI predicts f : OMEGA * K constantly, if there exists ann an n <OMEGA such that *J*[kn, (k+1)n)f(j)=PI(f|j)] holds, for any k < OMEGA.We denote by theta_k the smallest cardinality of a set of K- predictors psi which satisfies the following (*).
(*) For any omega*k, there exists a pi*psi such that pi predicts f constantly. It is an interesting problem that how large these theta^S are. Especially, compaired with the cardinals which were appeared in Cichon's diagram. Concerning this, we get the following results.
1. For any 2<less than or equal>K<less than or equal>M<less than or equal>omega, itholds that theta_k<less than or equa
2. cov(M) <less than or equal>theta_2 and cov(N) <less than or equal>theta_2.
3. non(N)<less than or equal>theta_<omega>
4. "cof(N)<theta_2" is consistent with ZFC.
5. "theta_<omega><d" is consistent with ZFC.
6. "theta_k<theta_<omega>", for all K <omega is consistent with ZFC.
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