*-Compactifications
The maximal semigroup of quotients of a finite semilattice.
Maximal (semi-)lattices of fractions and injective hulls.
Existentially closed domains with radical relations.
Decidability of the rings of real algebraic and p-adic algebraic integers.
Ordered fields and the ultrafilter theorem
We prove that on the basis of ZF the ultrafilter theorem and the theorem of Artin-Schreier are equivalent. The latter says that every formally real field admits a total order.
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