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- W3217585533 abstract "The departure point of this study is the fact that the well known Godel's theorems apply specifically to hypothetico-deductive systems - which I will rather call theories. Then it may be possible to turn around the dead-end identified by Godel, by trying to find other kinds of (with the condition that they shall not be equivalent to a deductive theory). So I will define theories and asymptotic theories. Chapter 1 and the thirteen following Memos lay down their foundations and present (Memo 4) the theory M : the Annexes A, B and C will prove that this theory is equivalent to usual Mathematics, i.e. [ZF] plus the axiom of foundation (AF) - but with no necessity to take into account the axiom of choice (AC). Using always the intuitive notion of dictives (Memo 10), the chapters 2 and 3 will introduce some new concepts: the superblocks of bounded letters, and the useful and sub-transitive dictives. The chapter 4 deals with a family of translative which are all consistent and leading to M. The unwritten chapter 5 hoped to finish the present work, but my age and other uncontrollable factors prevented me from a real success: I hope that other researchers will take over ..." @default.
- W3217585533 created "2021-12-06" @default.
- W3217585533 creator A5050447250 @default.
- W3217585533 date "2013-04-13" @default.
- W3217585533 modified "2023-09-25" @default.
- W3217585533 title "NE PEUT-ON PAS CONTOURNER L'IMPASSE IDENTIFIÉE PAR GÖDEL ET PROUVER LA CONSISTANCE DES MATHÉMATIQUES USUELLES ?" @default.
- W3217585533 hasPublicationYear "2013" @default.
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