Published February 20, 2026
| Version v1
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One True Foundation: Unity in Multiplicity
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We present abstraction logic, a foundation for formal mathematics and interactive theorem proving
that combines the single mathematical universe of first-order logic with the general variable
binding facility of higher-order logics. Its terms coincide with those of second-order equational
logic, but its unityped restriction yields a general and complete logic with elementary semantics.
Abstraction logic can naturally express a wide range of other logics while forming a coherent
whole and remaining closer to informal mathematics.
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