Logic II, 7.5 ECTS

Second level

Facts

Study pace 50%
Study time Daytime
Study form Normal
Language English
Special eligibility requirements
Admission to the course requires knowledge equivalent to 60 credits in mathematics. Admission also requires either the course Mathematics III - Logic, 7.5 credits (MM5024) or the two courses Metalogic: Completeness, 7.5 credits (FILOG3) and Metalogic: Incompleteness and undecidability, 7.5 credits (FILOG4), or equivalent.

Description

The course covers: • Fundamentals and set theory: The Zermelo-Fraenkel axioms of set theory, elementary theory for cardinals and ordinals. Equivalent formulations of the axiom of choice and its applications in analysis and algebra. • Structures…

The course covers: • Fundamentals and set theory: The Zermelo-Fraenkel axioms of set theory, elementary theory for cardinals and ordinals. Equivalent formulations of the axiom of choice and its applications in analysis and algebra. • Structures and models: Isomorphisms and embeddings, complete theories, elementary equivalence and elementary embedding, Löwenheim-Skolem’s theorems, categoricality, applications on algebraic theories and non-standard analysis. • Computability and incompleteness: Models of computation, classes of computable functions, decidable and irreversible problems, Gödel coding and Gödel’s incompleteness theorem.

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Area of interests: Information only in Swedish

Information only in Swedish

Subject

Mathematics

As a mathematical theory always implies that certain conclusions hold under certain given conditions, it can in principle say nothing about the physical reality. None the less mathematics has become an indispensable tool for a large number of subjects like astronomy, physics, chemistry, statistics and the technical sciences and in later times also for economy, biology, various social sciences and computor science. The role of mathematics in the applied sciences is both to supply notions for exact and adequate formulations of empirical laws but also from these laws to derive consequences, which can be used to find better models of the reality one has to describe. These tasks have lately become more important. Mathematics is in continual progress by intensive international research, new theories are created and already existing theories are simplified and augmented.

Mathematics

Course events

Autumn 2017

Study pace 50 %
Study time Daytime
Study form Normal
Language English.

Selection: No selection.

Start period: Period 2 - starts during the second half of the semester

Location: Stockholm

Additional information: Application deadline 18 April.

Tuition fee

Tuition fees only concern citizens outside the EU, EES and Switzerland
First instalment: 17500 SEK
Total course/programme fee: 17500 SEK

Tuition fees only concern citizens outside the EU, EES and Switzerland
Appl.code: SU-48022