On the Definitional Embeddability of the Combinatory Logic Theory into the First-Order Predicate Calculus

В. И. Шалак
2015 Logical Investigations  
In this article we prove a theorem on the definitional embeddability of the combinatory logic into the first-order predicate calculus without equality. Since all efficiently computable functions can be represented in the combinatory logic, it immediately follows that they can be represented in the first-order classical predicate logic. So far mathematicians studied the computability theory as some applied theory. From our theorem it follows that the notion of computability is purely logical.
more » ... s result will be of interest not only for logicians and mathematicians but also for philosophers who study foundations of logic and its relation to mathematics.
doi:10.21146/2074-1472-2015-21-2-9-14 fatcat:u64xyelytvfxlfbpu77y7lrwta