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Vieweg+Teubner Verlag Einführung in die Mathematische Logik: Teil II Prädikatenkalkül der Ersten Stufe: 19 (Mathematisch-Naturwissenschaftliche Bibliothek, 19)

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Description

Nachdem seit dem Erscheinen des ersten Teiles del' "Einfiihrung in die Mathematische Logik" me hI' als 12 Jahre vergangen sind, bin ich nun mehr in del' Lage, den zweiten Teil vorzulegen. Entsprechend dem ur sprunglichen Plan enthalt er die wichtigsten Ergebnisse iiber die Pradi katenlogik del' ersten Stufe, die hie I' konsequent als Logik (einsortiger) elementarer Sprachen entwickelt wird. Ich behandle dabei sofort den Pradikatenkalkiil mit Identitat und Operationssymbolen; die zum Teil abweichenden Ergebnisse fiir den Pradikatenkalkiil ohne Identitat er scheinen als Resultate iiber Ausdrucke und Ausdrucksmengen, in denen das Gleichheitszeichen nicht vorkommt. Das hat den Vorteil, daB die Pradikatenlogik del' ersten Stufe sofort in einer solchen Allgemeinheit aufgebaut wird, wie man sie in del' mathematischen Grundlagenforschung (Metamathematik) beim Studium formalisierter elementarer Theorien in del' Regel auch tatsachlich benotigt. Wie auch im ersten Tei!, geht es mil' VOl' allem um die Darstellung del' Wechselbeziehungen zwischen semantischen und syntaktischen Frage stellungen. Dabei habe ich mich insbesondere darum bemiiht, die Rolle des Modellbegriffs und des auf ihm basierenden Begriffs des logische'n Folgerns deutlich herauszuarbeiten. Ich halte den Folgerungsbegriff fiir den eigentlichen zentralen Begriff del' Logik, des sen formale (syntaktische) Erfassung das Hauptproblem del' mathematischen Logik darstellt. Dabei kommt diesel' formalen Erfassung in del' Pradikatenlogik wegen del' Nichtentscheidbarkeit d~r Folgerungsrelation, die allerdings erst im dritten Teil bewiesen wird, grundsatzliche Bedeutung zu.

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
01 September 1975
Listed Since
22 June 2013

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