Nepotpunost i neodlučivost aritmetike

Jelušić, Daniel (2015) Nepotpunost i neodlučivost aritmetike. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

The main goal of this thesis is proving Gödel’s incompleteness theorems, which establish fundamental limitations of provability in first-order theories. Additionally, we prove Tarski’s nondefinability theorem and Church’s undecidability theorem. In the first part, we describe the process of arithmetization and define arithmetical provability predicates. Next, we show that such predicates can be represented in all sufficiently strong theories, from which the results mentioned above immediately follow. Finally, we explore the provability of consistency and prove Gödel’s second incompleteness theorem.

Item Type: Thesis (Diploma thesis)
Supervisor: Vuković, Mladen
Date: 2015
Number of Pages: 46
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 20 Oct 2015 09:11
Last Modified: 20 Oct 2015 09:11
URI: http://digre.pmf.unizg.hr/id/eprint/4145

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