[1]朱慧灵,郑馥丹.马丁公理在基数不变量上的直接应用(英)[J].四川师范大学学报(自然科学版),2019,(06):739-745.[doi:10.3969/j.issn.1001-8395.2019.06.04]
 ZHU Huiling,ZHENG Fudan.Direct Application of Martin's Axiom on Cardinal Invariants[J].Journal of SichuanNormal University,2019,(06):739-745.[doi:10.3969/j.issn.1001-8395.2019.06.04]
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马丁公理在基数不变量上的直接应用(英)()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年06期
页码:
739-745
栏目:
基础理论
出版日期:
2019-11-04

文章信息/Info

Title:
Direct Application of Martin's Axiom on Cardinal Invariants
文章编号:
1001-8395(2019)06-0739-07
作者:
朱慧灵12 郑馥丹13
1.中山大学 数据科学与计算机学院, 广东 广州 510006; 2.三峡大学 三峡数学研究中心, 湖北 宜昌 443002; 3.华南理工大学 广州学院, 广东 广州 510800
Author(s):
ZHU Huiling12 ZHENG Fudan13
1.School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, Guangdong; 2.Three Gorges Mathematical Research Center, Three Gorges University, Yichang 443002, Hubei; 3.Guangzhou College, South China University of Technology, Guangzhou 510800, Guangdong
关键词:
马丁公理 基数不变量 柯恩力迫 随机力迫 局部马希斯力迫 赫奇勒力迫
Keywords:
Martin's axiom cardinal invariants Cohen forcing random forcing local mathias forcing Hechler forcing.
分类号:
O144.3
DOI:
10.3969/j.issn.1001-8395.2019.06.04
文献标志码:
A
摘要:
研究马丁公理和多种力迫偏序,解释如何直接应用马丁公理以决定实数集合上的基数不变量的取值.
Abstract:
In this paper, we study Martin's Axiom and various forcing partial orders and explain how Martin's Axiom can be directly applied to affect the value of the cardinal invariants of real number sets.

参考文献/References:

[1] COHEN P J.The independence of the continuum hypothesis[J].Proceedings of the National Academy of Sciences,1963,50(6):1143-1148.
[2] COHEN P J.The discovery of forcing[J].The Rocky Mountain J Mathematics,2002,32(4):1071-1100.
[3] KUNEN K.Set Theory an Introduction to Independence Proofs[M].London:Elsevier,2014.
[4] NIK W.Forcing for Mathematicians[M].Singapore:World Scientific,2014.
[5]MARTIN D A, SOLOVAY R M.Internal cohen extensions[J].Annals of Mathematical Logic,1970,2(2):143-178.
[6] FREMLIND H.Consequences of Martin's Axiom[M].London:Cambridge University Press,1988.
[7] KUNEN K.Set Theory:An Introduction to Independence Proofs[M].London:Elsevier,1980.
[8] BARTOSZYNSKI T.JUDAH H.Set Theory:on the Structure of the Real Line[M].Massachusetts:AK Peters/CRC Press,1995.
[9] 朱慧灵.关于单纯力迫和可数力迫的构造性阐述[J].四川师范大学学报(自然科学版),2017,40(1):18-21.
[10] BLASS A.Combinatorial Cardinal Characteristics of the Continuum[M].Handbook of set theory.Dordrecht:Springer,2010:395-489.
[11] MALLIARIS M, SHELAH S.Cofinality spectrum theorems in model theory, set theory, and general topology[J].J American Mathematical Society,2016,29(1):237-297.
[12] SOLOVAY R M.A model of set-theory in which every set of reals is Lebesgue measurable[J].The Annals of Mathematics,1970,92(1):1-56.
[13] MATHIAS A R D.Happy families[J].Annals of Mathematical Logic,1977,12(1):59-111.
[14] ZHU H L, ZHENG F D.Forcing an ω1-real without adding a real[J].J Mathematics,2017,37(05):911-915.
[15] HECHLER S H.On the existence of certain cofinal subsets of ωω.in axiomatic set theory:proceedings of the symposium in pure mathematics of the American mathematical society[C]//Rhode Island:American Mathematical Society,1974:155-173.
[16] PAWLIKOWSKI J.Why Solovay real produces Cohen real[J].J Symbolic Logic,1986,51(4):957-968.

备注/Memo

备注/Memo:
收稿日期: 2018-07-09 接受日期:2018-12-20 基金项目: 国家自然科学基金青年基金(11701592)、国家自然科学基金联合基金(U1811263)和广东省大数据分析与处理重点实验室项目 第一作者简介: 朱慧灵(1985—),男,博士,主要从事数理逻辑及其应用的研究,E-mail:zhuhling6@mail.sysu.edu.cn
更新日期/Last Update: 2019-11-04