ENGLISH

Formal Specification and Verification

By Schmitt P.H.

Book information

Language
english
Format
PDF
Filesize
454 kB (464413 bytes)
Pages
\152
Topic
Mathematics Logic
Library
twirpx
Time added
2017-08-07 07:01:42
Математика;Математическая логика;Теория множеств

Description

Published online. — 2006. — 152 p. English. (OCR-слой).[Prof. P.H. Schmitt. Fakultat fur Informatik. Universitat Karlsruhe (TH). Axiomatic Set Theory. Sommer 2006].Contents. Zermelo-Fraenkel (ZF) Axiom System (1): A1 Extensionality. A2 Foundation. A3 Subset. A4 Empty set. Zermelo-Fraenkel Axiom System (2): A5 Pair set. A6 Power set. A7 Sum. A8 Infinity. Zermelo-Fraenkel Axiom System (3): A9 Replacement. A10 Axiom of Choice. Class Terms. Class Terms as Sets. Some Abbreviations for Sets. Existence Claims. Lemma on Unions and Intersections. Proof of Existence of Intersections. Proof of Existence of Unions. Ordered Pairs. Relations and Functions. Existence Proofs. Natural Numbers N. Formal Definition of N. Peano’s Axioms. Proof of Axiom 4 Set Theoretic Properties of N. Transitive Sets. N is transitive. The order relation on N. Set Theoretic Properties of N (II). The Recursion Theorem. Uniqueness. Idea of Existence Proof. Details of Existence Proof. Addition of natural numbers. Multiplication of natural numbers. The Integers. The construction of Z. Operations on Z. Order Relation on Z.

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