Properties of ideals on the real line
Project/Area Number  09640288 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Osaka Prefecture University 
Principal Investigator 
KAMO Shizuo College of Integrated Arts and Sciences, Osaka Prefecture University, Professor, 総合科学部, 教授 (30128764)

Project Fiscal Year 
1997 – 1998

Project Status 
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 / 基数不変量 / 強制法 / evasion number / プレディクター / shrinkability 
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 Kpredictor. We say that a Kpredictor PI predicts f : OMEGA * K constantly, if there exists ann an n <OMEGA such that *J*[kn, (k+1)n)f(j)=PI(fj)] 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. 6. θ_ω<dはZFCと無矛盾である。

Report
(4results)
Research Output
(9results)