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Discernible elements in models for Peano arithmetic

Published online by Cambridge University Press:  12 March 2014

Andrzej Ehrenfeucht
Andrzej Ehrenfeucht*
Affiliation:
University of Colorado, Boulder, Colorado 80302
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Extract

Combinations of capital letters (e.g., G, EVEN) will be used as names of formulas of Peano arithmetic, x, y, z will be variables. Let be a model for Peano arithmetic. The names of formulas with a bar (e.g., G−, EVEN−(x)) will denote the relations defined by the formulas in . The elements of are called numbers.

By a finite sequence of numbers 〈a0, …, an〉 we mean a number . Note that n Pi's and ai's can be nonstandard elements and therefore “finite,” and all concepts which will use it are not absolute but relative to .

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 38 , Issue 2 , June 1973 , pp. 291 - 292
Copyright
Copyright © Association for Symbolic Logic 1973

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