Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A finitely axiomatizable undecidable
equational theory with recursively
solvable word problems


Author: Dejan Delic
Journal: Trans. Amer. Math. Soc. 352 (2000), 3065-3101
MSC (1991): Primary 03B25; Secondary 08A50, 08B05
DOI: https://doi.org/10.1090/S0002-9947-99-02339-9
Published electronically: October 5, 1999
MathSciNet review: 1615947
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we construct a finitely based variety, whose equational theory is undecidable, yet whose word problems are recursively solvable, which solves a problem stated by G. McNulty (1992). The construction produces a discriminator variety with the aforementioned properties starting from a class of structures in some multisorted language (which may include relations), axiomatized by a finite set of universal sentences in the given multisorted signature. This result also presents a common generalization of the earlier results obtained by B. Wells (1982) and A. Mekler, E. Nelson, and S. Shelah (1993).


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 03B25, 08A50, 08B05

Retrieve articles in all journals with MSC (1991): 03B25, 08A50, 08B05


Additional Information

Dejan Delic
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada
Email: ddelic@math.uwaterloo.ca

DOI: https://doi.org/10.1090/S0002-9947-99-02339-9
Keywords: Multisorted logic, universal theory, variety, equational theory, word problem
Received by editor(s): June 21, 1996
Received by editor(s) in revised form: January 8, 1998
Published electronically: October 5, 1999
Article copyright: © Copyright 2000 American Mathematical Society