Proof in Alonzo Church's and Alan Turing's Mathematical Logic: Undecidability of First-Order Logic - Paperback

by Jonathan O. Chimakonam (Ph D) (Author)

In the year 1900 the German Mathematician David Hilbert gave a curious address in Paris, at the meeting of the 2nd International Congress of Mathematicians - he titled his address "Mathematical Problems". In it, he emphasized the importance of taking on challenging problems for maintaining the progress and development of mathematics. The problems numbered 1, 2, and 10 which concern mathematical logic and which gave birth to what is called the entscheidungsproblem or the decision problem were eventually solved though in the negative by Alonzo Church and Alan Turing in their famous Church-Turing thesis. The later Turing and Gumanski's attempts are criticized as inadequate or doubtful. So the decision problem is still unsolved in the positive. This book provides a positive solution using what the author calls the General Theory of Effectively Provable Function (GEP). Tremendous insights on computer development and evolution also come to light in this research. Obviously, this book is an audacious attempt to solve a problem that has lasted for more than a century and defied the best minds of logic's greatest era!