Abstract
Aim of the lectures: to outline various methods used recently in construction of models for axioms of set theory. No completeness in pursuing this aim is attempted.
In the introductory lecture I we describe three systems of axioms for abstract set theory. In all these systems there are two primitive notions: “class” and “membership”. We define sets as classes which are capable of being members of other classes: x is a set if and only if there is a class y such that x ∈ y. We also define atoms as objects which have no elements.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mostowski, A. (2010). Models of Set Theory. In: Casari, E. (eds) Aspects of Mathematical Logic. C.I.M.E. Summer Schools, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11080-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-11080-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11078-8
Online ISBN: 978-3-642-11080-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)