Theory of pure equality
In mathematical logic the theory of pure equality is a first-order theory. It has a signature consisting of only the equality relation symbol, and includes no non-logical axioms at all (Monk 1976:240–242). This theory is consistent, as any set with the usual equality relation provides an interpretation.
The theory of pure equality was proven to be decidable by Löwenheim in 1915. If an additional axiom is added saying that there are exactly m objects for a fixed natural number m, or an axiom scheme is added saying that there are infinitely many objects, then the resulting theory is complete.
See also
References
- Monk, J. Donald (1976), Mathematical Logic, Graduate Texts in Mathematics, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90170-1
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