𝔖 Bobbio Scriptorium
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ALGEBRAIC CLOSURE WITHOUT CHOICE

✍ 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.

✦ 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.


πŸ“œ SIMILAR VOLUMES


Closure Algebras and Boolean Algebras
✍ G. J. Logan πŸ“‚ Article πŸ“… 1977 πŸ› John Wiley and Sons 🌐 English βš– 212 KB

## 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 € 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,, . . ., ,

On many-sorted algebraic closure operato
✍ Juan Climent Vidal; Juan Soliveres Tur πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 96 KB

## Abstract A theorem of Birkhoff‐Frink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the corresponding generated subalgebra operator. However, for many‐sorted sets, i.e., indexed families of sets, such a theorem is not longer

Closure Algebras and T1-Spaces
✍ G. J. Logan πŸ“‚ Article πŸ“… 1977 πŸ› John Wiley and Sons 🌐 English βš– 133 KB
Power Series and p-Adic Algebraic Closur
✍ Kiran S Kedlaya πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 181 KB

We describe a presentation of the completion of the algebraic closure of the ring of Witt vectors of an algebraically closed field of characteristic p>0. The construction uses ``generalized power series in p'' as constructed by Poonen, based on an example of Lampert, and also makes use of an analogo