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- Title
ITERATING SYMMETRIC EXTENSIONS.
- Authors
KARAGILA, ASAF
- Abstract
The notion of a symmetric extension extends the usual notion of forcing by identifying a particular class of names which forms an intermediate model of ZF between the ground model and the generic extension, and often the axiom of choice fails in these models. Symmetric extensions are generally used to prove choiceless consistency results. We develop a framework for iterating symmetric extensions in order to construct new models of ZF. We show how to obtain some well-known and lesser-known results using this framework. Specifically, we discuss Kinna–Wagner principles and obtain some results related to their failure.
- Subjects
ITERATED integrals; ITERATIVE methods (Mathematics); DEFINABILITY theory (Mathematical logic); AXIOMS; MATHEMATICAL analysis
- Publication
Journal of Symbolic Logic, 2019, Vol 84, Issue 1, p123
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2018.73