Nelson E. Predicative Arithmetic

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Princeton University Press, 1986, -201 pp.

The book is based on lecture notes of a course given at Princeton University in 1980. From the contents: the impredicativity of induction, the axioms of arithmetic, order, induction by relativization, the bounded least number principle, Euclidean algorithm, encoding, sets and functions, and more.

The impredicativity of induction
Logical terminology
The axioms of arithmetic
Order
Induction by relativization
Interpretability in Robinson's theory
Bounded induction
The bounded least number principle
The Euclidean algorithm
Encoding
Bounded separation and minimum
Sets and functions
Exponential functions
Exponentiation
A stronger relativization scheme
Bounds on exponential functions
Bounded replacement
An impassable barrier
Sequences
Cardinality
Existence of sets
Semibounded replacement
Formulas
Proofs
Derived rules of inference
Special constants
Extensions by definition
Interpretations
The arithmetization of arithmetic
The consistency theorem
Is exponentiation total?
A modjfied Hilbert program

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