Properties of ideals on the real line
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants|
General mathematics (including Probability theory/Statistical mathematics)
|Research Institution||Osaka Prefecture University|
KAMO Shizuo College of Integrated Arts and Sciences, Osaka Prefecture University, Professor, 総合科学部, 教授 (30128764)
|Project Period (FY)
1997 – 1998
Completed(Fiscal Year 1998)
|Budget Amount *help
¥2,100,000 (Direct Cost : ¥2,100,000)
Fiscal Year 1998 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1997 : ¥1,200,000 (Direct Cost : ¥1,200,000)
|Keywords||cardinal invariant / forcing / predictor / evasion numbers / プレディクター / shrinkability|
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.
Research Output (9results)