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Strictly Primitive Recursive Realizability, I
The Journal of Symbolic Logic
Vol. 59, No. 4 (Dec., 1994), pp. 1210-1227
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2275700
Page Count: 18
You can always find the topics here!Topics: Realizability, Induction assumption, Sequents, Recursion, Recursive functions, Logical proofs, Integers, Falsifiability, Mathematical functions, Mathematical induction
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A realizability notion that employs only primitive recursive functions is defined, and, relative to it, the soundness of the fragment of Heyting Arithmetic (HA) in which induction is restricted to Σ01 formulae is proved. A dual concept of falsifiability is proposed and an analogous soundness result is established for a further restricted fragment of HA.
The Journal of Symbolic Logic © 1994 Association for Symbolic Logic