I'd like to know what are quantifiers in game-based security definitions (in cryptography)

Some relevant examples and sources are also much appreciated.

Edit: for example, in a formal definition, we say for any security parameters, any function $F$, etc. My question is what should be included in these quantifiers (shall we include everything picked deterministically by the experiment?)is there any clear rule we need to follow?

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    $\begingroup$ A bit of context might be helpful. $\endgroup$ – Maeher Oct 19 at 10:12
  • $\begingroup$ @Maeher thanks for the comment! I have added more text. $\endgroup$ – Ay. Oct 19 at 10:19

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