Universality of the automorphism group of the real line期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Universality of the automorphism group of the real line

Authors:	Frieder Haug

Affiliation:	(1) Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany

Abstract:	We discuss the question, whether each automorphism group (of cardinality at most $2^{aleph _0 }$ ) of a linear order is embeddable into the automorphism group of the real line. We show that the answer to this question is independent of the axioms of ZFC: the answer is positive, if we assume $2^{aleph _0 }$ < $2^{aleph _1 }$ and Souslin's hypothesis; the answer is negative, if we assume $2^{aleph _0 } = 2^{aleph _1 }$ orV=L.

Keywords:	03E35
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