Forschungsarbeit: Intuitionistic Set Theory

Intuitionistic Set Theory

or How to construct semi-rings. Part IV

Forschungsergebnisse zur Informatik, Band 61

Hamburg , 280 Seiten

ISBN 978-3-8300-0691-6 (Print)

Zum Inhalt

The logical problem is an old problem. Leibniz developed a „mathesis universalis“, which he estimated to be the Logic of sciences. His approach was rational calculable. Frege took Leibniz‘s ideas and prepared a logic, which was composed by nitions.

In Frege‘s Logic the calculation with numbers plays an essential role. Frege thought that the arithmetic, which was known in his time, is a basis for a logic.

Finally David Hilbert continued the work by Leibniz-Frege. He tried to prove the consistency of mathematics by his predicate calculus. Hilbert worked with finite, decidable, mathematical procedures, as the author does.

Between the first and second volume of Hilbert‘s predicate calculus Kurt Gödel published his two incomplete propositions. He showed that the formalistic proofs by Hilbert cannot solve the consistency problem on principle; Gödel‘s result caused the crisis of the foundations of mathematics, which has done away with the Intuitionistic Set Theory.

  • Intuitionistic Set Theory, Part I: ISBN 3-86064-616-8
  • Intuitionistic Set Theory, Part II: ISBN 3-86064-617-6
  • Intuitionistic Set Theory, Part III: ISBN 3-8300-0378-1
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    Weitere Bücher des Autors

    : Intuitionistic Set Theory

    Intuitionistic Set Theory

    or How to construct semi-rings Part III

    Hamburg , ISBN 978-3-8300-0378-6 (Print)


    : Intuitionistic Set Theory Part II

    Intuitionistic Set Theory Part II

    Hamburg , ISBN 978-3-86064-617-5 (Print & eBook)


    : Intuitionistic Set Theory Part I

    Intuitionistic Set Theory Part I

    Hamburg , ISBN 978-3-86064-616-8 (Print & eBook)

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