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HILBERT, D. UND W. ACKERMANN. - THE FOUNDATION OF MODERN MATHEMATICAL LOGIC.
Grundzüge der theoretischen Logik.
Berlin, Springer, 1928. 8vo. Uncut in orig. printed wrappers. VIII,120. With the name of Bent Schultzer (Former Danish professor in philosophy) on first leaf. Internally clean.
Reference : 49908
First edition. (Die Grundlehren der Mathematischen Wissenshaften in Einzeldarstellungen, Band XXVII). In the years 1917-22 Hilbert gave three seminal courses at the Univeristy og Göttingen on logic and the foundation of mathematics. He received considerable help in preperation and eventual write up of these lectures from Bernays. This material was subsequently reworked by Ackermann into the monograph 'Grundzüge der Theoretischen Logik' (the offered item). It containes the first exposition ever of first-order logic and poses the problem of its completeness and the decision problem ('Entscheidungsproblem'). The first of these questions was answered just a year later by Kurt Gödel in his doctorial dissertation 'Die Vollständigkeit der Axiome des logischen Funktionenkalküls'. This result is known as Gödel's completeness theorem. Two years later Gödel published his famous 1931 paper 'Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I' in which he showed that a stronger logic, capable of modeling arithmetic, is either incomplete or inconsistent (Gödel's second incompleteness theorem). The later question posed by Hilbert and Ackermann regarding the decision problem was answered in 1936 independantly by Alonzo Church and Allan Turing. Church used his model the lambda-calculus and Turing his machine model to construct undecidable problems and show that the decision problem is unsolvable in first-order logic. These results by Gödel, Church, and Turing rank amongst the most important contributions to mathematical logic ever.
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William Schneider
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5 book(s) with the same title
Grundzüge der Theoretischen Logik. (Die Grundlehren der Mathematischen Wissenshaften in Einzeldarstellungen, Band XXVII).
Berlin, Julius Springer, 1928. 8vo. Publisher's full cloth. Ink signature of Samuel Skulsky on front free end paper. Completely clean throughout. A fine and tight copy.
First edition of the foundation of modern mathematical logic.In the years 1917-22 Hilbert gave three seminal courses at the Univeristy og Göttingen on logic and the foundation of mathematics. He received considerable help in preperation and eventual write up of these lectures from Bernays. This material was subsequently reworked by Ackermann into the monograph 'Grundzüge der Theoretischen Logik' (the offered item). It containes the first exposition ever of first-order logic and poses the problem of its completeness and the decision problem ('Entscheidungsproblem'). The first of these questions was answered just a year later by Kurt Gödel in his doctorial dissertation 'Die Vollständigkeit der Axiome des logischen Funktionenkalküls'. This result is known as Gödel's completeness theorem. Two years later Gödel published his famous 1931 paper 'Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I' in which he showed that a stronger logic, capable of modeling arithmetic, is either incomplete or inconsistent (Gödel's second incompleteness theorem). The later question posed by Hilbert and Ackermann regarding the decision problem was answered in 1936 independantly by Alonzo Church and Allan Turing. Church used his model the lambda-calculus and Turing his machine model to construct undecidable problems and show that the decision problem is unsolvable in first-order logic. These results by Gödel, Church, and Turing rank amongst the most important contributions to mathematical logic ever. Scarce in this condition.
HILBERT, D. UND W. ACKERMANN. - THE FOUNDATION OF MODERN MATHEMATICAL LOGIC.
Reference : 46101
(1928)
Grundzüge der theoretischen Logik.
Berlin, Springer, 1928. Orig. full cloth. Lower part of spine with loss of cloth. Lower right cornerof titlepage cut away, no loss of letters. VIII,120 pp.
First edition. (Die Grundlehren der Mathematischen Wissenshaften in Einzeldarstellungen, Band XXVII). In the years 1917-22 Hilbert gave three seminal courses at the Univeristy og Göttingen on logic and the foundation of mathematics. He received considerable help in preperation and eventual write up of these lectures from Bernays. This material was subsequently reworked by Ackermann into the monograph 'Grundzüge der Theoretischen Logik' (the offered item). It containes the first exposition ever of first-order logic and poses the problem of its completeness and the decision problem ('Entscheidungsproblem'). The first of these questions was answered just a year later by Kurt Gödel in his doctorial dissertation 'Die Vollständigkeit der Axiome des logischen Funktionenkalküls'. This result is known as Gödel's completeness theorem. Two years later Gödel published his famous 1931 paper 'Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I' in which he showed that a stronger logic, capable of modeling arithmetic, is either incomplete or inconsistent (Gödel's second incompleteness theorem). The later question posed by Hilbert and Ackermann regarding the decision problem was answered in 1936 independantly by Alonzo Church and Allan Turing. Church used his model the lambda-calculus and Turing his machine model to construct undecidable problems and show that the decision problem is unsolvable in first-order logic. These results by Gödel, Church, and Turing rank amongst the most important contributions to mathematical logic ever.
Grundzüge der theoretischen Logik. Zweite, verb. Aufl.
Berlin, Springer, 1938. Orig. printed wrappers. Wr. with tear in spine. VIII,134 pp.
Grundzüge der theoretischen Logik. Vierte Auflage.
Berlin, Göttingen..., Springer-Verlag, 1959. Orig. full cloth. VIII,188 pp. A few underlinings and notes.
Grundzüge der theoretischen Logik. Dritte, verb. Aufl.
Berlin, Springer, 1949. Orig. full cloth. A few brownspots to covers. A small stamp on foot of titlepage. VIII,156 pp.
