FOM: Re: Quantifier question

[Jay Halcomb]

----- Original Message -----
From: "Torkel Franzen" <torkel at sm.luth.se>
To: <fom at math.psu.edu>
Sent: Friday, July 12, 2002 08:55
Subject: FOM: Quantifier question

>...concerning the logic with "there are infinitely many x such that" as its
only
> quantifier...
>   Does anybody have any ideas about this, or about any treatment of it
> in the literature? I haven't been able to find any such treatment.

The following references are older but useful sources:

Monk, Mathematical Logic, Chapter 30, "Finitary Extensions [Cardinality
Quantifiers]", has a short discussion of generalized/cardinality
quantifiers, with references.

Bell and Slomson, Models and Ultraproducts, Ch. 13, "Generalized
Quantifiers", has a longer discussion of generalized/cardinality
quantifiers, with references.

Jay Halcomb
Interests: logic and computability.
<http://www.sonic.net/~halcomb>