I.o. operator
From Apstheory
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[edit] Definition
[edit] 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.
[edit] 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
.
