Solutions for Exercises in Unit 1
Exercise 4.3.10
Consider the type
. This type must be finitely satisfiable, because
there actually is an greater than all of any finite set of rationals. By a previous
exercise, must be satisfiable. Since is saturated, is satisfiable in . The proof for
infinitely small elements is similar. For the isolation of
, we can also make types
and
.
Both are satisfied in , as above. Then is the unique rational in the interval between
any realization of and any realization of .
Saylor URL: http://www.saylor.org/MA201 Subunit 1.4.3
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