Mathematical LogicUndergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilberttype proof theory, and proof theory handled through derived rules. Part II supplements the material covered in Part I and introduces some of the newer ideas and the more profound results of logical research in the twentieth century. Subsequent chapters introduce the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Gödel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Gödel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. Unabridged republication of the edition published by John Wiley & Sons, Inc. New York, 1967. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index. 
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Review: Mathematical Logic
User Review  Ryan O'neil  GoodreadsGreat book, but one piece of advice before you read; find a PDF or introtocourse online that introduces some of the basic concepts because the author jumps right in pretty quickly. Read full review
Contents
I  3 
II  8 
III  13 
IV  17 
V  20 
VI  22 
VII  25 
VIII  28 
XXXIII  180 
XXXIV  183 
XXXV  186 
XXXVI  191 
XXXVII  198 
XXXVIII  201 
XXXIX  215 
XL  223 
IX  33 
X  39 
XI  43 
XII  45 
XIII  50 
XIV  58 
XV  67 
XVI  74 
XVII  83 
XVIII  93 
XIX  96 
XX  101 
XXI  107 
XXII  112 
XXIII  116 
XXIV  121 
XXV  125 
XXVI  134 
XXVII  140 
XXVIII  148 
XXIX  151 
XXX  157 
XXXI  167 
XXXII  175 
Common terms and phrases
1(A V B A D B A V B applied argument assignment assume assumption formulas atoms Axiom Schema axiomatic calculus with equality called ChurchTuring thesis completeness theorem computation consistency consistency proof contain x free countably inﬁnite counterexample D P(x Dintrod decision problem deduction theorem deﬁned deﬁnition domain enumeration equality axioms establish Example Exercise expressions Fpart ﬁnd ﬁnite ﬁrst formal system free occurrences free variables function symbols Gentzen given Godel's Hilbert inference integers interpretation intuitionistic ions Kleene Lemma lines logical function mathematics mesons metamathematics method model theory modus ponens natural numbers nonlogical axioms notation number theory numbertheoretic object language postulates predicate calculus predicate parameter predicate symbols proof theory propositional calculus provable proved quantiﬁers real numbers recursive replace result rules satisﬁable sequent Similarly simply speciﬁcally substitution true truth table Turing machine Vrule valid consequence Vx3yP(x VxA(x VxP(x VxQ(x