I.o. operator

From Apstheory

Contents 1 Definition 1.1 Symbol-free definition 1.2 Definition with symbols 2 See also

Definition

Symbol-free definition

The i.o. operator or infinitely often operator is an operator from the group property space to the group APS property space that takes a group property and returns the property of being an APS of groups for which infinitely many members satisfy the given group property.

Definition with symbols

The i.o. operator or infinitely often operator is an operator from the group property space to the group APS property space that takes a group property and returns the property Failed to parse (Can't write to or create math temp directory): i.o.(p)

defined as follows:

An APS Failed to parse (Can't write to or create math temp directory): G

of groups satisfies Failed to parse (Can't write to or create math temp directory): i.o.(p)
if there are infinitely many Failed to parse (Can't write to or create math temp directory): n
for which Failed to parse (Can't write to or create math temp directory): G_n
satisfies Failed to parse (Can't write to or create math temp directory): p

.

See also

• Eventually operator