Notation: "infinity" superscript on universal quantifier

Hey guys,

I've come across a some notation that I have not seen before and since it's all symbols, I couldn't really find anything on Google about it. I don't think it's necessary/relevant to explain the entire context here, but the formula read like this:

where COINF if the index set of all coinfinite recursively enumerable sets.

It's probably not all that complicated, but I've never seen the quantifier notation before. What does it mean? The variable is supposed to range over the natural numbers.

Thank you!

Selinde

Re: Notation: "infinity" superscript on universal quantifier

I know what recursively enumerable sets are, but I don't think is a universally accepted notation. I believe it should have been defined earlier in your text. If it were , it could mean that there exist infinitely many objects. Maybe means "for all y's that are indices of infinite recursively enumerable sets"? If your text is available online, I could look into it.

Re: Notation: "infinity" superscript on universal quantifier

The text is available here: http://arxiv.org/pdf/1302.7069v1.pdf -- the notation first occurs on the bottom of page 8 and is not defined earlier. That's why I assumed I was just missing some knowledge (as is usually the case when I'm reading these things ;) ) The meaning that you suggested is a possibility, but I do not yet understand the proof enough to check this.

Edit: I think it might mean "for all but finitely many", could this be correct?