Gödel's Incompleteness Theorem

By V.A. Uspenskij

The booklet is provided with six applications written somewhat more concisely, although still does not assume any specialized knowledge. The first one addresses the issue of the relationship between the presence of true and unprovable statements with allegations that are neither provable nor refutable. The second proved a strengthening of G del's theorem - a theorem Tarski's concept of truth inexpressible. The third is devoted to the justification of the application of one of the axioms of the theory of algorithms, contained in 5, namely, the axioms of arithmetic. To this end, we introduce a particular class of algorithms - a class of targeted programs - and checked Arithmetic functions computed algorithms of this class. In the fourth application developed in 2 of the criteria for completeness and incompleteness applied to the language associated with the so-called associative calculus. The fifth application is dedicated to the original wording of the incompleteness theorem, proposed by Godel. Sixth app contains exercises to some of the previous sections. Finally, the last appendix contains the answers to the exercises and instructions. Applications are independent of each other and can be read in any order, except for Annex B, which require some space exploring introduced in Appendix B concepts.

• Format: Paperback
• Language: Russian
• ISBN: 5519435618
• ISBN13: 9785519435611
• Release Date: April 2015
• Publisher: Book on Demand Ltd.
• Length: 116 Pages
• Weight: 0.35 lbs.
• Dimensions: 0.3" x 5.8" x 8.3"