Wolfgang Rautenberg
g
A Concise Introduction to
g g g
Mathematical Logic g
Textbook Thir g
d Edition
g
Typesetg andg layout:g Theg authorgV
ersiong fromg Juneg 2009gcorrections
g included
,
,Foreword
byg Levg Beklemishev,g Moscow
Thegfieldgofgmathematicalglogic—
evolvinggaroundgthegnotionsgofglogicalgvalidity,gprovability,gandgcomputatio
n—
wasgcreatedgingthegfirstghalfgofgthegpreviousgcenturygbygagcohortgofgbrilliantg
mathematiciansgandgphilosophersgsuchgasgFrege,gHilbert,gGödel,gTuring,gTa
rski,gMalcev,gGentzen,gandgsomegothers.gThegdevelopmentgofgthisgdisciplin
egisgarguablygamonggtheghighestgachievementsgofgsciencegingthegtwentiethgc
entury:g itgexpandedgmathe-
gmatics gintogagnovel garea gofgapplications, gsubjected glogical greasoning gandgco
mputabilitygtogrigorousganalysis,gandgeventuallygledgtogthegcreationgofgcomp
uters.
ThegtextbookgbygProfessorgWolfganggRautenberggisgagwell-writtengin-
gtroduction gtogthis gbeautiful gandgcoherent gsubject. g Itgcontains gclassicalgmate
rialgsuchgasglogicalgcalculi,gbeginningsgofgmodelgtheory,gandgGödel’sgincom
pletenessgtheorems,gasgwellgasgsomegtopicsgmotivatedgbygapplica-
gtions, g suchgasgagchapter gonglogicgprogramming. g The gauthor ghasgtakeng grea
tgcaregtogmakegthegexpositiongreadablegandgconcise;geachgsectiongisgaccomp
aniedgbygaggoodgselectiongofgexercises.
Agspecialgwordgofgpraisegisgduegforgthegauthor’sgpresentationgofgGödel’sgs
econdgincompletenessgtheorem,gingwhichgthegauthorghasgsucceededginggivin
gg ang accurateg andg simpleg proofg ofg theg derivabilityg conditionsg andgthegpr
ovablegΣ1-
completeness,gagtechnicallygdifficultgpointgthatgisgusuallygomittedgingtextboo
ksgofgcomparableglevel.g Thisgworkgcangbegrecommendedgtog allg studentsg wh
og wantg tog learng theg foundationsg ofg mathematicalg logic.
, v
g
A Concise Introduction to
g g g
Mathematical Logic g
Textbook Thir g
d Edition
g
Typesetg andg layout:g Theg authorgV
ersiong fromg Juneg 2009gcorrections
g included
,
,Foreword
byg Levg Beklemishev,g Moscow
Thegfieldgofgmathematicalglogic—
evolvinggaroundgthegnotionsgofglogicalgvalidity,gprovability,gandgcomputatio
n—
wasgcreatedgingthegfirstghalfgofgthegpreviousgcenturygbygagcohortgofgbrilliantg
mathematiciansgandgphilosophersgsuchgasgFrege,gHilbert,gGödel,gTuring,gTa
rski,gMalcev,gGentzen,gandgsomegothers.gThegdevelopmentgofgthisgdisciplin
egisgarguablygamonggtheghighestgachievementsgofgsciencegingthegtwentiethgc
entury:g itgexpandedgmathe-
gmatics gintogagnovel garea gofgapplications, gsubjected glogical greasoning gandgco
mputabilitygtogrigorousganalysis,gandgeventuallygledgtogthegcreationgofgcomp
uters.
ThegtextbookgbygProfessorgWolfganggRautenberggisgagwell-writtengin-
gtroduction gtogthis gbeautiful gandgcoherent gsubject. g Itgcontains gclassicalgmate
rialgsuchgasglogicalgcalculi,gbeginningsgofgmodelgtheory,gandgGödel’sgincom
pletenessgtheorems,gasgwellgasgsomegtopicsgmotivatedgbygapplica-
gtions, g suchgasgagchapter gonglogicgprogramming. g The gauthor ghasgtakeng grea
tgcaregtogmakegthegexpositiongreadablegandgconcise;geachgsectiongisgaccomp
aniedgbygaggoodgselectiongofgexercises.
Agspecialgwordgofgpraisegisgduegforgthegauthor’sgpresentationgofgGödel’sgs
econdgincompletenessgtheorem,gingwhichgthegauthorghasgsucceededginggivin
gg ang accurateg andg simpleg proofg ofg theg derivabilityg conditionsg andgthegpr
ovablegΣ1-
completeness,gagtechnicallygdifficultgpointgthatgisgusuallygomittedgingtextboo
ksgofgcomparableglevel.g Thisgworkgcangbegrecommendedgtog allg studentsg wh
og wantg tog learng theg foundationsg ofg mathematicalg logic.
, v
