Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Set Theory
Date
2018
Author
Kaya, Burak
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
365
views
0
downloads
Cite This
Language and axioms of set theory. Ordered pairs, relations and functions. Order relation and well ordered sets. Ordinal numbers, transfinite induction, arithmetic of ordinal numbers. Cardinality and arithmetic of cardinal numbers. Axiom of choice, generalized continuum hypothesis.
URI
https://ocw.metu.edu.tr/course/view.php?id=270
https://hdl.handle.net/11511/37062
Collections
Department of Mathematics, Course Material
Suggestions
OpenMETU
Core
Smooth manifolds with infinite fundamental group admitting no real projective structure
Çoban, Hatice; Ozan, Yıldıray; Department of Mathematics (2017)
In this thesis, we construct smooth manifolds with the infinite fundamental group Z_2*Z_2, for any dimension n>=4, admitting no real projective structure. They are first examples of manifolds in higher dimensions with infinite fundamental group admitting no real projective structures. The motivation of our study is the related work of Cooper and Goldman. They proved that RP^3#RP^3 does not admit any real projective structure and this is the first known example in dimension 3.
Mathematical ontology the question of the mathematical source of objectivity
Dorrikhteh, Omid; Grünberg, David; Department of Philosophy (2019)
This thesis traces the source of mathematical objectivity, as an approach to justify mathematical properties to be real, through how our mind and language were evolved. In the mirror of the indispensability argument, and the unreasonable effectiveness of mathematics, it will be argued that the reason why the world and the mind exhibit ontologically similar structures (and properties) is because they have the same ontological origin. Accordingly, it will be shown that (1) why/how that “the world and the mind...
Time-dependent recursion operators and symmetries
Gurses, M; Karasu, Atalay; Turhan, R (Informa UK Limited, 2002-05-01)
The recursion operators and symmetries of nonautonomous, (1 + 1) dimensional integrable evolution equations are considered. It has been previously observed hat he symmetries of he integrable evolution equations obtained through heir recursion operators do not satisfy the symmetry equations. There have been several attempts to resolve his problem. It is shown that in the case of time-dependent evolution equations or time-dependent recursion operators associativity is lost. Due to this fact such recursion ope...
Classical double copy: Kerr-Schild-Kundt metrics from Yang-Mills theory
GÜRSES, METİN; Tekin, Bayram (American Physical Society (APS), 2018-12-28)
The classical double copy idea relates some solutions of Einstein's theory with those of gauge and scalar field theories. We study the Kerr-Schild-Kundt (KSK) class of metrics in d dimensions in the context of possible new examples of this idea. We first show that it is possible to solve the Einstein-Yang-Mills system exactly using the solutions of a Klein-Gordon-type scalar equation when the metric is the pp-wave metric, which is the simplest member of the KSK class. In the more general KSK class, the solu...
Normalizers in homogeneous symmetric groups
Güven, Ülviye Büşra; Kuzucuoğlu, Mahmut; Department of Mathematics (2017)
We study some properties of locally finite simple groups, which are the direct limit of finite (finitary) symmetric groups of (strictly) diagonal type. The direct limit of the finite (finitary) symmetric groups of strictly diagonal type is called textbf{homogeneous (finitary) symmetric groups}. In cite{gkk}, Kegel, Kuzucuou{g}lu and myself studied the structure of centralizer of finite groups in the homogeneous finitary symmetric groups. Instead of strictly diagonal embeddings, if we have diagonal embedding...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
B. Kaya, “Set Theory,” 00, 2018, Accessed: 00, 2020. [Online]. Available: https://ocw.metu.edu.tr/course/view.php?id=270.