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Selected topic from Set Theory - NMAG537

Title:	Vybraná témata z teorie množin
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. Mgr. Radek Honzík, Ph.D.
Class:	M Mgr. MSTR M Mgr. MSTR > Povinně volitelné
Classification:	Mathematics > Algebra

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (10.06.2021)

This is a follow up cours for the basic set theory courses intended for master and PhD students.

Course completion requirements -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (24.05.2021)

Credit will be awarded for active participation.

Literature -

Last update: doc. Mgr. Radek Honzík, Ph.D. (29.09.2022)

B. Balcar, P. Štěpánek, Teorie množin, Academia, Praha 2001.

T. Jech, Set Theory: The Third Millennium Edition, revised and expanded, Springer, 2003.

A. Kanamori, The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings (Springer Monographs in Mathematics) 2nd Edition, Springer 2008.

K. Kunen, Set Theory (Studies in Logic: Mathematical Logic and Foundations), College Publications; Revised ed. edition (November 2, 2011).

M. Foreman, A. Kanamori (Eds), Handbook of Set Theory 2010th Edition, Vols 1-3, Springer 2010.

Syllabus -

Last update: doc. Mgr. Radek Honzík, Ph.D. (06.09.2022)

Topics:

Combinatorics on uncountable regular cardinals, Aronszajn a Suslin trees, stationary reflection and its different versions. Combinatorics on successors of singular cardinals. Large cardinals and their basic properties (Mahlo cardinals, weakly compact cardinals, measurable cardinals, etc.), connections between large cardinals and combinatorics on cardinals omega_2, omega_3, etc. Connections with the Continuum Hypothesis (CH) and the properties of the real line. Proper Forcing Axiom and its consequences.