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MINIMAL AXIOMATIC FRAMEWORKS FOR DEFINABLE HYPERREALS WITH TRANSFER

Published online by Cambridge University Press:  01 May 2018

FREDERIK S. HERZBERG ,
VLADIMIR KANOVEI ,
MIKHAIL KATZ  and
VASSILY LYUBETSKY
FREDERIK S. HERZBERG
Affiliation:
CENTER FOR MATHEMATICAL ECONOMICS (IMW) INSTITUTE FOR INTERDISCIPLINARY STUDIES OF SCIENCE (I2SOS) BIELEFELD UNIVERSITY, UNIVERSITÄTSSTRAßE 25 D-33615 BIELEFELD, GERMANY and MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY (MCMP) LUDWIG MAXIMILIAN UNIVERSITY OF MUNICH GESCHWISTER-SCHOLL-PLATZ 1 D-80539 MUNICH, GERMANY E-mail: [email protected]
VLADIMIR KANOVEI
Affiliation:
LABORATORY 6 IITP, MOSCOW, RUSSIA and DEPARTMENT OF MATHEMATICS INSTITUTE OF ECONOMICS AND FINANCE MIIT, MOSCOW, RUSSIA E-mail: [email protected]
MIKHAIL KATZ
Affiliation:
DEPARTMENT OF MATHEMATICS BAR ILAN UNIVERSITY RAMAT GAN 5290002, ISRAEL E-mail: [email protected]
VASSILY LYUBETSKY
Affiliation:
LABORATORY 6 IITP, MOSCOW, RUSSIA E-mail: [email protected]
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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

03E3503C20definabilityhyperrealsuperstructure
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 385 - 391
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

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