Aufgrund von Vorbereitungen auf eine neue Version von KOPS, können derzeit keine Publikationen eingereicht werden. (Due to preparations for a new version of KOPS, no publications can be submitted currently.)

On a diophantine representation of the predicate of provability

Cite This

Files in this item

Files Size Format View

There are no files associated with this item.

CARL, Merlin, Boris Zelikovich MOROZ, 2014. On a diophantine representation of the predicate of provability. In: Journal of Mathematical Sciences. 199(1), pp. 36-52. ISSN 1072-3374. eISSN 1573-8795. Available under: doi: 10.1007/s10958-014-1830-2

@article{Carl2014dioph-21343.2, title={On a diophantine representation of the predicate of provability}, year={2014}, doi={10.1007/s10958-014-1830-2}, number={1}, volume={199}, issn={1072-3374}, journal={Journal of Mathematical Sciences}, pages={36--52}, author={Carl, Merlin and Moroz, Boris Zelikovich} }

2018-02-05T14:52:02Z 2014 Carl, Merlin On a diophantine representation of the predicate of provability Carl, Merlin Moroz, Boris Zelikovich eng Moroz, Boris Zelikovich 2018-02-05T14:52:02Z Let P be the first-order predicate calculus with a single binary predicate letter. Making use of the techniques of Diophantine coding developed in the works on Hilbert’s tenth problem, we construct a polynomial F(t; x1, . . . , xn) with integral rational coefficients such that the Diophantine equation<br />F(t<sub>0</sub>;x<sub>1</sub>,…, x<sub>n</sub>)=0<br />is soluble in integers if and only if the formula of P numbered t0 in the chosen numbering of the formulas of P is provable in P. As an application of that construction, we describe a class of Diophantine equations that can be proved insoluble only under some additional axioms of the axiomatic set theory, for instance, assuming the existence of an inaccessible cardinal. Bibliography: 14 titles. terms-of-use

This item appears in the following Collection(s)

Version History

Version Item Date Summary Publication Version

*Selected version

Search KOPS


My Account