Equivalenze tra teoremi: il programma di ricerca della reverse mathematics
Marcone, Alberto
La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematica Italiana, Tome 2 (2009), p. 101-126 / Harvested from Biblioteca Digitale Italiana di Matematica
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La logica matematica ha sviluppato strumenti in grado di rendere precise affermazioni del tipo «il teorema A è più forte del teorema B». In particolare sono stati ottenuti un consistente numero di risultati che stabiliscono la forza assiomatica di molti teoremi in diversi settori della matematica. I risultati in questione hanno dato origine ad un programma di ricerca noto con il nome di reverse mathematics. Nel presente articolo evidenziamo gli «antenati» della reverse mathematics, descriviamo lo stato attuale della ricerca, e illustriamo il significato della reverse mathematics per i fondamenti della matematica.

Mathematical Logic can give a precise meaning to statements of the form «Theorem A is stronger than Theorem B». In the last few decades logicians have proved many results about the axiomatic strength of theorems from different areas of mathematics. These results form a research project known as reverse mathematics. In this paper we discuss the antecedents of reverse mathematics, describe the current research in the area, and elucidate the import of reverse mathematics upon the foundations of mathematics.

Publié le : 2009-04-01
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     author = {Alberto Marcone},
     title = {Equivalenze tra teoremi: il programma di ricerca della reverse mathematics},
     journal = {La Matematica nella Societ\`a e nella Cultura. Rivista dell'Unione Matematica Italiana},
     volume = {2},
     year = {2009},
     pages = {101-126},
     zbl = {1186.03020},
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     url = {http://dml.mathdoc.fr/item/RIUMI_2009_1_2_1_101_0}
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Marcone, Alberto. Equivalenze tra teoremi: il programma di ricerca della reverse mathematics. La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematica Italiana, Tome 2 (2009) pp. 101-126. http://gdmltest.u-ga.fr/item/RIUMI_2009_1_2_1_101_0/

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