4

"The Härtig quantifier captures a certain fairly large fragment of second-order logic and contributes to understanding higher-order logic." (p. 1154 http://www.jstor.org/stable/2275466?seq=1#page_scan_tab_contents)

By the Härtig quantifier I mean the equicardinality quantifier defined on the first page of the above article.

What fragment of second-order logic does the quantifier capture?

Secondly, if we add the Härtig quantifier to first order logic, what metalogical properties of first order logic (Compactness, completeness, etc) are lost? (answer found: it loses compactness and is not axiomatizable)

user65526
  • 1,373
  • The article you link actually answers your questions. For example $\mathcal{L}(I)$ it is neither compact, (in fact not countably compact) nor axiomatizable. – abc May 19 '15 at 10:50
  • 1
    Ok, but what fragment of second-order logic does it capture? – user65526 May 19 '15 at 11:33

0 Answers0