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# ðŸ“™ Metamathematics, machines and Goedel's proof by N. Shankar â€” free epub

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The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While G?del's first incompleteness theorem showed that no computer program could automatically prove certain true theorems in mathematics, the advent of electronic computers and sophisticated software means in practice there are many quite effective systems for automated reasoning that can be used for checking mathematical proofs. This book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including those of G?del and Church-Rosser. The computer verification using the Boyer-Moore theorem prover yields precise and rigorous proofs of these difficult theorems. It also demonstrates the range and power of automated proof checking technology. The mechanization of metamathematics itself has important implications for automated reasoning, because metatheorems can be applied as labor-saving devices to simplify proof construction.

## About book:

## About file:

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- Series:
**Cambridge Tracts in Theoretical Computer Science 38** - Author:
**N. Shankar** - Year:
**1994** - Publisher:
**Cambridge University Press** - Language:
**English** - ISBN:
**052142027X,0511569882,9780521585330,9780521420273,9780511569883,0521585333**

- DPI:
**300** - File size:
**1 423 164** - Format:
**djvu**

Security code:

The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While GÃ¶del's first incompleteness theorem showed that no computer program could automatically prove certain true theorems in mathemat...

The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While G?del's first incompleteness theorem showed that no computer program could automatically prove certain true theorems in mathemat...

Proof technology will become an established field in software engineering. It generally aims at integrating proof processing into industrial design and verifications tools. The origins of this technology lie in the systematic understanding of a fully-fled...

This book describes the specification and proof of a compiler for a realistically complicated assembly-level language. The book defines the state of the art in machine check proofs of software. Piton is a simple assembly-level programming language fo...

As the complexity of embedded computer-controlled systems increases, the present industrial practice for their development gives cause for concern, especially for safety-critical applications where human lives are at stake. The use of software in such sys...

Pt. I. The Theory of Machine Proof. 1. Geometry Preliminaries. 2. The Area Method. 3. Machine Proof in Plane Geometry. 4. Machine Proof in Solid Geometry. 5. Vectors and Machine Proofs -- Pt. II. Topics From Geometry: A Collection of 400 Mechanically Pr...

Pt. I. The Theory of Machine Proof. 1. Geometry Preliminaries. 2. The Area Method. 3. Machine Proof in Plane Geometry. 4. Machine Proof in Solid Geometry. 5. Vectors and Machine Proofs -- Pt. II. Topics From Geometry: A Collection of 400 Mechanically Pr...

Computation is revolutionizing our world, even the inner world of the "pure" mathematician. Mathematical methods - especially the notion of proof - that have their roots in classical antiquity have seen a radical transformation since the 1970s, as success...

Too many network administrators depend on the "big sky" principle of network security - they believe that the large number of Internet-connected machines out there will keep black-hat hackers away. Hack Proofing Your Network: Internet Tradecraft points ou...