Single axioms for groups |
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Authors: | Kenneth Kunen |
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Affiliation: | (1) Computer Sciences Department, University of Wisconsin, 53706 Madison, WI, USA |
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Abstract: | We study equations of the form (=x) which are single axioms for group theory. Earlier examples of such were found by Neumann and McCune. We prove some lower bounds on the complexity of these , showing that McCune's examples are the shortest possible. We also show that no such can have only two distinct variables. We do produce an with only three distinct variables, refuting a conjecture of Neumann. Automated reasoning techniques are used both positively (searching for and verifying single axioms) and negatively (proving that various candidate (=x) hold in some nongroup and are, hence, not single axioms). |
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Keywords: | Group model paramodulation |
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