Elements of set theory and recursive arguments
In this paper we provide a self-contained introduction to some of the basic topics of Mathematical Analysis, comprising natural and unrestricted set theoretic methods. The note reflects partially the contents of a lecture given by the second author during the International Workshop on New Horizons i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Accademia Peloritana dei Pericolanti
2021-09-01
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| Series: | Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| Online Access: |
http://dx.doi.org/10.1478/AAPP.99S1A17
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| _version_ | 1819032894097588224 |
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| author | Giuseppe Devillanova Giovanni Molica Bisci |
| author_facet | Giuseppe Devillanova Giovanni Molica Bisci |
| author_sort | Giuseppe Devillanova |
| collection | DOAJ |
| description | In this paper we provide a self-contained introduction to some of the basic topics of
Mathematical Analysis, comprising natural and unrestricted set theoretic
methods. The note reflects partially the contents of a lecture given by the second author during the International Workshop on New Horizons in Teaching Science in Messina on June 2018. More precisely, following a quite new didactic approach, we recall here some basic facts on the Generalized Induction Principle as well as the Recursion Theorem, which plays a crucial role in the foundation of Mathematical Logic. Some elements of von Neumann, Gödel and Bernays (NGB) set theory are given in the last section. The note provides the preliminary tools that are essential in order to study the classical notion of Dedekind completeness. |
| first_indexed | 2024-12-21T07:09:11Z |
| format | Article |
| id | doaj.art-dc3d86477faa409fae92dfe5fcda4795 |
| institution | Directory Open Access Journal |
| issn | 0365-0359 1825-1242 |
| language | English |
| last_indexed | 2024-12-21T07:09:11Z |
| publishDate | 2021-09-01 |
| publisher | Accademia Peloritana dei Pericolanti |
| record_format | Article |
| series | Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| spelling | doaj.art-dc3d86477faa409fae92dfe5fcda47952022-12-21T19:12:01ZengAccademia Peloritana dei PericolantiAtti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali0365-03591825-12422021-09-0199S1A1710.1478/AAPP.99S1A17AAPP.97S1A17Elements of set theory and recursive argumentsGiuseppe DevillanovaGiovanni Molica BisciIn this paper we provide a self-contained introduction to some of the basic topics of Mathematical Analysis, comprising natural and unrestricted set theoretic methods. The note reflects partially the contents of a lecture given by the second author during the International Workshop on New Horizons in Teaching Science in Messina on June 2018. More precisely, following a quite new didactic approach, we recall here some basic facts on the Generalized Induction Principle as well as the Recursion Theorem, which plays a crucial role in the foundation of Mathematical Logic. Some elements of von Neumann, Gödel and Bernays (NGB) set theory are given in the last section. The note provides the preliminary tools that are essential in order to study the classical notion of Dedekind completeness. http://dx.doi.org/10.1478/AAPP.99S1A17 |
| spellingShingle | Giuseppe Devillanova Giovanni Molica Bisci Elements of set theory and recursive arguments Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| title | Elements of set theory and recursive arguments |
| title_full | Elements of set theory and recursive arguments |
| title_fullStr | Elements of set theory and recursive arguments |
| title_full_unstemmed | Elements of set theory and recursive arguments |
| title_short | Elements of set theory and recursive arguments |
| title_sort | elements of set theory and recursive arguments |
| url |
http://dx.doi.org/10.1478/AAPP.99S1A17
|
| work_keys_str_mv | AT giuseppedevillanova elementsofsettheoryandrecursivearguments AT giovannimolicabisci elementsofsettheoryandrecursivearguments |