FOM: Query on strengths of statements
Colin McLarty
cxm7 at po.cwru.edu
Fri Apr 14 14:29:02 EDT 2000
Can someone summarize what is known about the strength of the following
statements? Thanks.
Colin McLarty
1) The field of rationals Q has an algebraic closure.
2) The field of rationals has an extension field of infinite transcendence
degree.
3) A countably infinite transcendence degree extension of Q has an
algebraic closure.
4) The field C of all complex numbers has an extension of infinite
transcendence degree.
5) A countably infinite transcendence degree extension of C has an
algebraic closure.
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