NONCONSTRUCTIVIZABLE FORMAL ARITHMETIC STRUCTURES
A A Tverskoĭ · Mathematics of the USSR-Izvestiya · 1988
Nonconstructivizability of a number of formal arithmetric structures is established in nonstandard models of formal Peano arithmetric (PA). Also considered is a formal structure whose constructivizability in a countable nonstandard model of PA depends on the choice of the model. All concrete examples are built on formulas of class Δ1(PA). Therefore the standard interpretations are recursive. Bibliography: 12 titles.