FOM: Query on strengths of statements

[Colin McLarty]

	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.