DIPLOMA "The completeness and consistency of the theory" (the author's work, mathematics, theory of algorithms)

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Uploaded: 22.01.2008
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The diploma in mathematics
on the topic:
"The completeness and consistency of"

Jobs gave up in 2004 in the Tula State Pedagogical University
named Leo Tolstoy, in the Faculty of Mathematics and Informatics at 5 ("excellent").
The paper deals with aspects of the mathematical logic and theory of algorithms.

This work is never and nowhere so far not spread, and nowhere
It spreads. You will be the first and only its owner!

- Introduction;
- Chapter I. axiomatic-deductive method and the emergence of a formal axiomatic;
- Chapter II. Formal arithmetic S and its system of axioms;
- 2.1. Egalitarian theory;
- 2.2. The language and the rules of inference of formal arithmetic;
- Chapter III. Elements of the theory of algorithms and computable functions;
- 3.1. The concept of algorithm and computable function;
- 3.2. Recursive functions and relations;
- 3.3. Arithmetic functions and relationships. Betta function Gödel;
- 3.4. Arithmetization. Godel numbers. Church's thesis;
- 3.5. Markov normal algorithms;
- 3.6. Turing algorithms;
- Chapter IV. The incompleteness of formal arithmetic;
- 4.1. Existence is not computable functions;
- 4.2. Undecidability formal arithmetic.
Godel's incompleteness theorem;
- 4.3. Recursively enumerable sets;
- 4.4. The proof of the consistency of formal arithmetic;
- Conclusion;
- References;

In this study, very, very many formulas! In this regard, sometimes Word'a
from this is simply "mind-blowing!" So in this archive is a diploma, divided into parts (by chapters).

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