Abstract
This historical note illuminates how Leon Henkin’s work influenced that of the author. It focuses on Henkin’s development of a formulation of type theory based on equality, and the significance of this contribution.
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Notes
- 1.
- 2.
In both propositional type theory and full type theory (as we shall use these terms), the types are generated inductively from basic types by the condition that if α and β are types, then (αβ) is the type of functions with arguments of type β and values of type α. In propositional type theory, the only basic type is the type 0 of truth values, but in full type theory, the basic types are 0 and a type ι of individuals. Thus, propositional type theory may be regarded as higher-order propositional calculus, while full type theory includes nth-order logic for each positive integer n.
- 3.
The proof has not yet been published.
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Andrews, P.B. (2014). A Bit of History Related to Logic Based on Equality. In: Manzano, M., Sain, I., Alonso, E. (eds) The Life and Work of Leon Henkin. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-09719-0_8
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