Strongly proper sub-APS

From Apstheory

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This article describes a property that can be evaluated for a sub-APS of an APS and uses only set-theoretical properties

[edit] Definition

[edit] Symbol-free definition

A sub-APS is termed strongly proper in the APS if there are infinitely many indices for which the sub-APS member is a proper subset of the APS member.

[edit] Definition with symbols

A sub-APS Failed to parse (Can't write to or create math temp directory): H

of an APS Failed to parse (Can't write to or create math temp directory): G
is termed strongly proper if there are infinitely many indices 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): H_n
is a proper subset of Failed to parse (Can't write to or create math temp directory): G_n

.

Any proper saturated sub-APS is strongly proper.