Programme

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.

Core Documentation

V. Michele Abrusci e Lorenzo Tortora de Falco, Logica. Vol. 1 Dimostrazioni e modelli al primo ordine, Springer, 2014

Type of delivery of the course

The course includes Face-to-face lectures; Discussions with students and debates on the discussed topics; Exercices; Attendance is not mandatory but strongly recommended. In case of health emergency due to COVID-19 the way lectures will be given will depend on the conditions. In such a potential framework all the possible efforts will be done to limit the unavoidable damages related to the necessity to switch to online courses and interaction during the lessons will be preserved as much as possible. The lessons will be broadcasted live and won't be recorded.

Type of evaluation

Written and/or oral exam, of a duration usually between 30 and 45 minutes. In case of health emergency due to COVID-19 the way exams will be held will depend on the conditions. In such a potential framework all the possible efforts will be done to limit the unavoidable damages related to the necessity to switch to online exams.

Programme

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.

Core Documentation

V. Michele Abrusci e Lorenzo Tortora de Falco, Logica. Vol. 1 Dimostrazioni e modelli al primo ordine, Springer, 2014

Type of delivery of the course

The course includes Face-to-face lectures; Discussions with students and debates on the discussed topics; Exercices; Attendance is not mandatory but strongly recommended. In case of health emergency due to COVID-19 the way lectures will be given will depend on the conditions. In such a potential framework all the possible efforts will be done to limit the unavoidable damages related to the necessity to switch to online courses and interaction during the lessons will be preserved as much as possible. The lessons will be broadcasted live and won't be recorded.

Type of evaluation

Written and/or oral exam, of a duration usually between 30 and 45 minutes. In case of health emergency due to COVID-19 the way exams will be held will depend on the conditions. In such a potential framework all the possible efforts will be done to limit the unavoidable damages related to the necessity to switch to online exams.

Programme

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.

Core Documentation

V. Michele Abrusci e Lorenzo Tortora de Falco, Logica. Vol. 1 Dimostrazioni e modelli al primo ordine, Springer, 2014

Type of delivery of the course

The course includes Face-to-face lectures; Discussions with students and debates on the discussed topics; Exercices; Attendance is not mandatory but strongly recommended. In case of health emergency due to COVID-19 the way lectures will be given will depend on the conditions. In such a potential framework all the possible efforts will be done to limit the unavoidable damages related to the necessity to switch to online courses and interaction during the lessons will be preserved as much as possible. The lessons will be broadcasted live and won't be recorded.

Type of evaluation

Written and/or oral exam, of a duration usually between 30 and 45 minutes. In case of health emergency due to COVID-19 the way exams will be held will depend on the conditions. In such a potential framework all the possible efforts will be done to limit the unavoidable damages related to the necessity to switch to online exams.