Eventually operator

From Apstheory

[edit] Definition

[edit] Symbol-free definition

The eventually 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 all but finitely many members satisfy the given group property.

[edit] Definition with symbols

The eventually operator is an operator from the group property space to the group APS property space, that given a group property Failed to parse (Can't write to or create math temp directory): p

returns the property Failed to parse (Can't write to or create math temp directory): Ev(p)

, defined as follows:

An APS of groups Failed to parse (Can't write to or create math temp directory): (G,\\Phi)

satisfies Failed to parse (Can't write to or create math temp directory): Ev(p)
if there exists an Failed to parse (Can't write to or create math temp directory): n
such that 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): Ev(p)
for all Failed to parse (Can't write to or create math temp directory): N > n

.