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UNCOUNTABLE REAL CLOSED FIELDS WITH PA INTEGER PARTS

Published online by Cambridge University Press:  22 April 2015

DAVID MARKER,
JAMES H. SCHMERL and
CHARLES STEINHORN
DAVID MARKER
Affiliation:
DEPARTMENT OF MATHEMATICS, STATISTICS, AND COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT CHICAGO 851 S. MORGAN ST., CHICAGO, IL 60607-7045, USAE-mail: marker@math.uic.edu
JAMES H. SCHMERL
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CONNECTICUT 196 AUDITORIUM RD U-3009 STORRS, CT 06269-3009, USAE-mail: schmerl@math.uconn.edu
CHARLES STEINHORN
Affiliation:
DEPARTMENT OF MATHEMATICS VASSAR COLLEGE 124 RAYMOND AVENUE, BOX 257 POUGHKEEPSIE, NY 12604-0257, USAE-mail: steinhorn@vassar.edu
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Abstract

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D’Aquino, Knight, and Starchenko classified the countable real closed fields with integer parts that are nonstandard models of Peano Arithmetic. We rule out some possibilities for extending their results to the uncountable and study real closures of ɷ1-like models of PA.

Keywords

real closed fieldPeano arithmeticrecursively saturated modelɷ1-like model

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 2 , June 2015, pp. 490 - 502
Copyright
Copyright © The Association for Symbolic Logic 2015 

References

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