LEADER 04984nam 22015255 450 001 9910154750903321 005 20190708092533.0 010 $a1-4008-8200-1 024 7 $a10.1515/9781400882007 035 $a(CKB)3710000000620168 035 $a(MiAaPQ)EBC4738781 035 $a(DE-B1597)467917 035 $a(OCoLC)979728674 035 $a(DE-B1597)9781400882007 035 $a(EXLCZ)993710000000620168 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aTheory of Formal Systems. (AM-47), Volume 47 /$fRaymond M. Smullyan 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$dİ1961 215 $a1 online resource (157 pages) $cillustrations 225 0 $aAnnals of Mathematics Studies ;$v301 300 $a"A revision of the author's recent doctoral dissertation--[Princeton]." 311 $a0-691-08047-X 320 $aIncludes bibliography. 327 $tFrontmatter -- $tTABLE OF CONTENTS -- $tPREFACE -- $tANNALS OF MATHEMATICS STUDIES -- $tCHAPTER I: FORMAL MATHEMATICAL SYSTEMS -- $tCHAPTER II: FORMAL REPRESENTABILITY AND RECURSIVE ENUMERABILITY -- $tCHAPTER III: INCOMPLETENESS -AND UNDECIDABILITY -- $tCHAPTER IV: RECURSIVE FUNCTION THEORY -- $tCHAPTER V: CREATIVITY AND EFFECTIVE INSEPARABILITY -- $tSUPPLEMENT: APPLICATIONS TO MATHEMATICAL LOGIC -- $tREFERENCE AND BRIEF BIBLIOGRAPHY 330 $aThis book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems. 410 0$aAnnals of mathematics studies ;$vno. 47. 606 $aRecursive functions 606 $aMetamathematics 610 $aAddition. 610 $aAlgebraic geometry. 610 $aAlonzo Church. 610 $aArithmetic function. 610 $aArithmetic. 610 $aAtomic sentence. 610 $aAxiom A. 610 $aAxiom schema. 610 $aAxiom. 610 $aAxiomatic system. 610 $aBinary relation. 610 $aCantor's diagonal argument. 610 $aCartesian product. 610 $aCharacterization (mathematics). 610 $aChinese remainder theorem. 610 $aClosed-form expression. 610 $aClosure (mathematics). 610 $aCombination. 610 $aCombinatory logic. 610 $aComplement (set theory). 610 $aConcatenation theory. 610 $aConsistency. 610 $aConstructive proof. 610 $aCorollary. 610 $aCountable set. 610 $aCounterexample. 610 $aDecidability (logic). 610 $aDecision problem. 610 $aDefinable set. 610 $aDiagonalization. 610 $aDirect proof. 610 $aDisjoint sets. 610 $aEnumeration. 610 $aEquation. 610 $aExistential quantification. 610 $aExponential function. 610 $aFinite set. 610 $aFormal system. 610 $aFunctional calculus. 610 $aGödel numbering. 610 $aGödel's incompleteness theorems. 610 $aHerbrand's theorem. 610 $aInference. 610 $aInteger factorization. 610 $aIteration. 610 $aJohn Myhill. 610 $aLogical connective. 610 $aLogical consequence. 610 $aMathematical induction. 610 $aMathematical logic. 610 $aMathematician. 610 $aMathematics. 610 $aMetamathematics. 610 $aModus ponens. 610 $aNatural number. 610 $aNegation. 610 $aNumber theory. 610 $aOrder theory. 610 $aParity (mathematics). 610 $aPeano axioms. 610 $aPredicate (mathematical logic). 610 $aPrenex normal form. 610 $aPrimitive recursive function. 610 $aQuantifier (logic). 610 $aRecursion. 610 $aRecursive set. 610 $aRecursively enumerable set. 610 $aRemainder. 610 $aRequirement. 610 $aRule of inference. 610 $aScientific notation. 610 $aSequence. 610 $aSet (mathematics). 610 $aSign (mathematics). 610 $aSpecial case. 610 $aSubset. 610 $aSuggestion. 610 $aSystem U. 610 $aTheorem. 610 $aTheory. 610 $aTransfinite number. 610 $aTuring machine. 610 $aUniversal set. 610 $aValidity. 610 $aVariable (mathematics). 610 $aZermelo set theory. 615 0$aRecursive functions. 615 0$aMetamathematics. 676 $a511.33 700 $aSmullyan$b Raymond M., $050650 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154750903321 996 $aTheory of Formal Systems. (AM-47), Volume 47$92788798 997 $aUNINA