# 104.645 AKLOG Iterated Forcing This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2024S

2024S, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture
• Format: Presence

## Learning outcomes

After successful completion of the course, students are able to...

explain and judiciously apply the following concepts: properties of generic reals, composition of forcing notions, direct and projective limit of forcing iterations, preservation theorems (in particular: chain conditions, properness, w^w-bounding, axiom A)

## Subject of course

We first review the main concepts and theorems from the forcing method: dense sets, maximal antichains, names, generic filters, the forcing theorem. Then we consider several classical examples of forcing notions such as Cohen, random, Sacks, Mathias, as well as finite products and compositions of forcing notions.

The main topics will be transfinite iterations of forcing notions, with finite and countable supports (ccc or proper iterations, respectively).  Applications: Suslin's conjecture, Martin's Axiom, the Borel conjecture.

If some time is left, we will also consider the Levy collapse and Solovay's models.

## Teaching methods

Lecture at the blackboard.

Oral

## Course dates

DayTimeDateLocationDescription
Mon16:00 - 18:0004.03.2024 - 24.06.2024Sem.R. DB gelb 05 B 16-18
Tue10:00 - 12:0014.05.2024Sem.R. DA grün 06B may 14 only
AKLOG Iterated Forcing - Single appointments
DayDateTimeLocationDescription
Mon04.03.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon11.03.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon18.03.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon08.04.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon15.04.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon22.04.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon29.04.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon06.05.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon13.05.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Tue14.05.202410:00 - 12:00Sem.R. DA grün 06B may 14 only
Mon27.05.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon03.06.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon10.06.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon17.06.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18
Mon24.06.202416:00 - 18:00Sem.R. DB gelb 05 B 16-18

oral exam

Not necessary

## Curricula

Study CodeObligationSemesterPrecon.Info
860 GW Optional Courses - Technical Mathematics Mandatory elective

## Literature

No lecture notes are available.

## Previous knowledge

ZFC axioms, ZFC models, basics of forcing.

## Language

if required in English