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An Application of Logic to Combinatorial Geometry: How Many Tetrahedra are Equidecomposable with a Cube?

 

作者: Vladik Kreinovich,   Olga Kosheleva,  

 

期刊: Mathematical Logic Quarterly  （WILEY Available online 1994）
卷期: Volume 40, issue 1  

页码: 31-34

 

ISSN:0942-5616

 

年代: 1994

 

DOI:10.1002/malq.19940400105

 

出版商: WILEY‐VCH Verlag Berlin GmbH

 

关键词: Equidecomposability;Elementary Geometry;Generalized Quantifier

 

数据来源: WILEY

 

摘要:

AbstractIt is known (see Rapp [9]) that elementary geometry with the additional quantifier “there exist uncountably many” is decidable. We show that this decidability helps in solving the following problem from combinatorial geometry: does there exist an uncountable family of pairwise non‐congruent tetrahedra that aren‐equidecomposable with a cube?Mathematics Subject Classification:03B25, 03C80, 51M04, 52B05

 

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