Mathematical Logic Quarterly

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

Journal Article


It 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 are n‐equidecomposable with a cube?

Mathematics Subject Classification: 03B25, 03C80, 51M04, 52B05, 52B10.

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