Incomparable families and maximal trees

被引：4

作者：

Campero-Arena, G. ^{[1
]}

Cancino, J. ^{[2
]}

Hrusak, M. ^{[3
]}

Miranda-Perea, F. E. ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Fac Ciencias, Ciudad Univ, Mexico City 04510, DF, Mexico

[2] Univ Nacl Autonoma Mexico, Ctr Ciencias Matemat, AP 61-3, Morelia, Michoacan, Mexico

[3] Univ Nacl Autonoma Mexico, Inst Matemat, Area Invest Cient, Ciudad Univ, Mexico City 04510, DF, Mexico

来源：

FUNDAMENTA MATHEMATICAE | 2016年 / 234卷 / 01期

关键词：

Boolean algebra; antichain; incomparable family; tree; cardinal invariant; ALMOST-DISJOINT FAMILIES; BOOLEAN-ALGEBRAS; ANTICHAINS; CHAINS;

D O I：

10.4064/fm125-1-2016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We answer several questions of D. Monk by showing that every maximal family of pairwise incomparable elements of P(omega)/fin has size continuum, while it is consistent with the negation of the Continuum Hypothesis that there are maximal subtrees of both P(omega) and P(omega)/fin of size omega(1).

引用

页码：73 / 89

页数：17

共 20 条

[1] Combinatorics of dense subsets of the rationals [J].

Balcar, B ;

Hernández-Hernández, F ;

Hrusák, M .

FUNDAMENTA MATHEMATICAE, 2004, 183 (01) :59-80

[2] CHAINS AND ANTICHAINS IN P(OMEGA) [J].

BAUMGARTNER, JE .

JOURNAL OF SYMBOLIC LOGIC, 1980, 45 (01) :85-92

[3]

Blass A., 2010, HDB SET THEORY, P395, DOI [10.1007/978-1-4020-5764-9_7, DOI 10.1007/978-1-4020-5764-9_7]

[4] NARROW BOOLEAN-ALGEBRAS [J].

BONNET, R ;

SHELAH, S .

ANNALS OF PURE AND APPLIED LOGIC, 1985, 28 (01) :1-12

[5] SELF-DUAL UNIFORM MATROIDS ON INFINITE SETS [J].

Bowler, Nathan ;

Geschke, Stefan .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (02) :459-471

[6]

BRENDLE J, 2000, QUESTIONS ANSWERS GE, V18, P123

[7]

Cancino J., 2013, IRREDUNDANT GENERATO

[8] SEPARABILITY PROPERTIES OF ALMOST-DISJOINT FAMILIES OF SETS [J].

ERDOS, P ;

SHELAH, S .

ISRAEL JOURNAL OF MATHEMATICS, 1972, 12 (02) :207-&

[9] CLASSIFYING ALMOST-DISJOINT FAMILIES WITH APPLICATIONS TO BETAN - N [J].

HECHLER, SH .

ISRAEL JOURNAL OF MATHEMATICS, 1971, 10 (04) :413-&

[10] Cardinal invariants of analytic P-ideals [J].

Hernandez-Hernandez, Fernando ;

Hrusak, Michael .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2007, 59 (03) :575-595

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