# Set theory and forcing, 7.5 ECTS

Second level

## Facts

Study pace 25%
Study time Daytime
Study form Normal
Language English
Course code MM8027

## Syllabus

Special eligibility requirements
Admission to the course requires knowledge equivalent to at least 90 credits in mathematics, including the course Logic 7.5 credits (MM7008) or another basic course in logic covering the completeness theorem of predicate logic. English B/English 6 or equivalent.

## Description

The course covers modern set theory, models and independence results for axioms.

Classic set theory: Axioms of Zermelo-Fraenkels set theory (ZF). Ordinals, well-orderings and cardinal theory in ZF. Independence results for ZF: Permutation model…

The course covers modern set theory, models and independence results for axioms.

Classic set theory: Axioms of Zermelo-Fraenkels set theory (ZF). Ordinals, well-orderings and cardinal theory in ZF. Independence results for ZF: Permutation models and independence of the axiom of choice. Forcing and independence of the continuum hypothesis. Boolean-valued models. Consequences of the independence results within mathematics. A selection of the following topics: Infinitary combinatorics, Gödel´s constructible sets and the constructibility axiom. Alternative axioms: Projective determinacy and Martin’s axiom. Large cardinals. Constructive set theory: CZF and IZF.

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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

### Spring 2018

Study pace 25 %
Study time Daytime
Study form Normal
Language English.

Selection: No selection.

Start period: Period 1 - starts during the first half of the semester

Location: Stockholm