000 03826nam a22005055i 4500
001 978-0-387-34241-2
003 DE-He213
005 20161121231026.0
007 cr nn 008mamaa
008 100301s2006 xxu| s |||| 0|eng d
020 _a9780387342412
_9978-0-387-34241-2
024 7 _a10.1007/0-387-34241-9
_2doi
050 4 _aT57-57.97
072 7 _aPBW
_2bicssc
072 7 _aMAT003000
_2bisacsh
082 0 4 _a519
_223
100 1 _aRautenberg, Wolfgang.
_eauthor.
245 1 2 _aA Concise Introduction to Mathematical Logic
_h[electronic resource] /
_cby Wolfgang Rautenberg.
250 _a2.
264 1 _aNew York, NY :
_bSpringer New York,
_c2006.
300 _aXVIII, 256 p. 8 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext
505 0 _aPropositional Logic -- Predicate Logic -- Gödel’s Completeness Theorem -- The Foundations of Logic Programming -- Elements of Model Theory -- Incompleteness and Undecidability -- On the Theory of Self-Reference.
520 _aTraditional logic as a part of philosophy is one of the oldest scientific disciplines. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, Russell and others to create a logistic foundation for mathematics. It steadily developed during the 20th century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. While there are already several well-known textbooks on mathematical logic, this book is unique in that it is more concise than most others; the material is treated in a streamlined fashion. This allows the lecturer to select the material for a one-semester course on a topic more easily. Although the book is intended for use as a graduate text, the first three chapters could be understood by undergraduates interested in mathematical logic. These initial chapters cover just the material for an introductory course on mathematical logic combined with the necessary material from set theory. Chapter 3 is partly of a descriptive nature, providing a view towards decision problems, automated theorem proving, non-standard models and related subjects. The other chapters contain material on logic programming for computer scientists, model theory, recursion theory, Gödel's Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed where appropriate. The author has provided exercises for each section, as well as hints or even complete solutions to most exercises at the end of the book. From the foreword, written by Lev Beklemishev: "…a well-written introduction to this beautiful and coherent subject. It contains classical material such as logical calculi, beginnings of model theory, and Gödel’s incompleteness theorems, as well as some topics motivated by applications, such as a chapter on logic programming. The author has taken great care to make the exposition readable and concise.".
650 0 _aMathematics.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 0 _aComputer mathematics.
650 0 _aMathematical logic.
650 1 4 _aMathematics.
650 2 4 _aApplications of Mathematics.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aComputational Science and Engineering.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387302942
830 0 _aUniversitext
856 4 0 _uhttp://dx.doi.org/10.1007/0-387-34241-9
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c507470
_d507470