Minimal axiomatic frameworks for definable hyperreals with transfer
Logic
2018-05-14 v1
Abstract
We modify the definable ultrapower construction of Kanovei and Shelah (2004) to develop a ZF-definable extension of the continuum with transfer provable using countable choice only, with an additional mild hypothesis on well-ordering implying properness. Under the same assumptions, we also prove the existence of a definable, proper elementary extension of the standard superstructure over the reals. Keywords: definability; hyperreal; superstructure; elementary embedding.
Keywords
Cite
@article{arxiv.1707.00202,
title = {Minimal axiomatic frameworks for definable hyperreals with transfer},
author = {Frederik S. Herzberg and Vladimir Kanovei and Mikhail G. Katz and Vassily Lyubetsky},
journal= {arXiv preprint arXiv:1707.00202},
year = {2018}
}
Comments
8 pages, to appear in Journal of Symbolic Logic