## S(z A y ) z S(A), by (c) * S(z) A S(Y) 2 S(A) e S(x) 2 S(A) and S(y) 2 S(A) e C ( s ) s C ( A ) 'and C ( y ) E C ( A ) , by (c) o x β¬ C ( A ) and Y E C ( A ) . Now every ultrafilter is consistent and closed with respect to C, since if U is an ultrafilter and C ( U ) = X , then C({,uu,, . . ., ,
ALGEBRAIC CLOSURE WITHOUT CHOICE
β Scribed by Bernhard Banaschewski
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 178 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
This note shows that for the proof of the existence and uniqueness of the algebraic closure of a field one needs only the Boolean Ultrafilter Theorem.
π SIMILAR VOLUMES
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