To acquire a good knowledge of first order classical logic and its fundamental theorems.
Curriculum
scheda docente
materiale didattico
Programma
Proof of the compactness theorem for languages of any cardinality. Languages with equality. The compactness theorem for languages with equality. Correctness and completeness for languages with equality. L"owenheim-Skolem's theorem for (denumerable) languages with equality. The limits of the expressive power of first order languages. Elementary equivalence, substructures, elementary substructures. Isomorphsims and elementary equivalence. The notion of substructure. Elementary substructures and diagrams. The preservation theorems. Generalisations of the L"owenheim-Skolem's theorem. Completeness of a theory.Testi Adottati
V. Michele Abrusci e Lorenzo Tortora de Falco, Logica. Vol. 1 Dimostrazioni e modelli al primo ordine, Springer, 2014Modalità Erogazione
The course includes Face-to-face lectures; Discussions with students and debates on the discussed topics; Exercices; Attendance is not mandatory but strongly recommended.Modalità Frequenza
Attendance is not mandatory but strongly recommended.Modalità Valutazione
Written and/or oral exam, of a duration usually between 30 and 45 minutes.
scheda docente
materiale didattico
Mutuazione: 20410451-2 LM410 -TEOREMI SULLA LOGICA 1 - MODULO B in Matematica LM-40 TORTORA DE FALCO LORENZO
Programma
Proof of the compactness theorem for languages of any cardinality. Languages with equality. The compactness theorem for languages with equality. Correctness and completeness for languages with equality. L"owenheim-Skolem's theorem for (denumerable) languages with equality. The limits of the expressive power of first order languages. Elementary equivalence, substructures, elementary substructures. Isomorphsims and elementary equivalence. The notion of substructure. Elementary substructures and diagrams. The preservation theorems. Generalisations of the L"owenheim-Skolem's theorem. Completeness of a theory.Testi Adottati
V. Michele Abrusci e Lorenzo Tortora de Falco, Logica. Vol. 1 Dimostrazioni e modelli al primo ordine, Springer, 2014Modalità Erogazione
The course includes Face-to-face lectures; Discussions with students and debates on the discussed topics; Exercices; Attendance is not mandatory but strongly recommended.Modalità Frequenza
Attendance is not mandatory but strongly recommended.Modalità Valutazione
Written and/or oral exam, of a duration usually between 30 and 45 minutes.