Groups With Solvable Word Problems (Classic Reprint) - Hardcover

Semeniuk, Christine

9780331786002: Groups With Solvable Word Problems (Classic Reprint)

Hardcover

ISBN 10: 0331786001 ISBN 13: 9780331786002

Publisher: Forgotten Books, 2017

Excerpt from Groups With Solvable Word Problems

Equating truth in G with derivability from a set of axioms suggests the possibility of formulating the word problem for G as the derivability problem for some type of formal system. The first part of the paper is concerned with this. Once this is done, we can consider the questions usually asked about formal systems, such as consistency, decid ability, and completeness, and use results about particular formal systems to obtain results about groups and semigroups corresponding to these systems. In this analogy, nontrivial groups correspond to consistent systems, groups with solvable word problem to decidable systems, and simple groups to complete systems. The last analogy is particularly striking, for, strangely enough, although it has been known for a long time that complete recursively axiomatized theories are decidable, it was only recently noted that recursively presented simple groups have solvable word problems.

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