Beginner's Further Guide To Mathematical Logic, A

This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results.The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a 'fein' chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a 'decision machine.' Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic.This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics.

Aceasta carte este o continuare a Ghidului pentru incepatori pentru logica matematica. Volumul anterior trateaza elemente ale logicii propozitionale si de ordinul intai, contine un pic despre sistemele formale si recursivitatea si se incheie cu capitole despre celebra teorema a incompletitudinii lui Gödel, impreuna cu rezultatele conexe. .Volumul actual incepe cu ceva mai mult despre logica propozitionala si de ordinul intai, urmat de ceea ce as numi un capitol „fein”, care generalizeaza simultan unele rezultate din teoria recursivitatii, sisteme aritmetice de ordinul intai si ceea ce numesc „ masina de decizie. ' Apoi vin cinci capitole despre sistemele formale, teoria recursivitatii si aplicatiile metamatematice intr-un cadru general.