“Theory of pure equality”的意思、由来-开放百科全书

词条

Theory of pure equality

释义

References

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.

References

{{Citation | last1=Monk | first1=J. Donald | title=Mathematical Logic | publisher=Springer-Verlag | location=Berlin, New York | series=Graduate Texts in Mathematics | isbn=978-0-387-90170-1 | year=1976}}

1 : Formal theories

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。