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THE TRANSCENDENCE DEGREE OF THE REALS OVER CERTAIN SET-THEORETICAL SUBFIELDS

Part of: Connections with logic Set theory

Published online by Cambridge University Press:  04 March 2025

AZUL FATALINI Open the ORCID record for AZUL FATALINI [Opens in a new window]  and
RALF SCHINDLER Open the ORCID record for RALF SCHINDLER [Opens in a new window]
AZUL FATALINI*
Affiliation:
INSTITUT FÜR MATHEMATISCHE LOGIK UND GRUNDLAGENFORSCHUNG UNIVERSITÄT MÜNSTER MÜNSTER, GERMANY E-mail: rds@uni-muenster.de
RALF SCHINDLER
Affiliation:
INSTITUT FÜR MATHEMATISCHE LOGIK UND GRUNDLAGENFORSCHUNG UNIVERSITÄT MÜNSTER MÜNSTER, GERMANY E-mail: rds@uni-muenster.de
*
E-mail: azul.fatal@uni-muenster.de
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Abstract

It is a well-known result that, after adding one Cohen real, the transcendence degree of the reals over the ground-model reals is continuum. We extend this result for a set X of finitely many Cohen reals, by showing that, in the forcing extension, the transcendence degree of the reals over a combination of the reals in the extension given by each proper subset of X is also maximal. This answers a question of Kanovei and Schindler [2].

Keywords

transcendence degreetranscendence basesubfield of the realsalgebraically independentCohen reals

MSC classification

Primary: 03E99: None of the above, but in this section
Secondary: 12L99: None of the above, but in this section

Information

Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 18
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

REFERENCES

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