19

enter image description here

I could not find the yellow marked symbols with Detexify, nor in the Comprehensive LaTeX symbols list. Are these symbols even supported by latex?

  • 1
    They seem to be from some fraktur font. Where does this come from? – Bernard Sep 13 '14 at 15:11
  • 3
    @Bernard its in the famous article from about incompleteness by Kurt Gödel from 1930 – Adam Sep 13 '14 at 15:12
  • @Mico I haven't seen the term "deutsche Buchstaben" for Fraktur letters before. It seems about as accurate as the CJK tradition of calling letters of the Latin alphabet "English letters". – Sverre Sep 13 '14 at 15:28
  • @Sverre -- I suppose that by the early XXth century, the only (major) country in Europe where gothic/fraktur/schwabacher lettering was still in use was Germany. That's probably why Gödel called them "deutsche Buchstaben", right? Observe that the family of "German" font faces really comprised three distinct subgroups: Fraktur proper, Schwabacher, and Gothic. The letters used in the screenshot definitely belong to the Fraktur subcategory. – Mico Sep 13 '14 at 15:41
  • 2
    @Mico, I understand why the term is used. But I just think of Fraktur as "old style", as it was widely used in my country (Norway) in the 19th century. And in Norway, "Fraktur" is called "Gothic script", just to add to the confusion :) And Norway is clearly a major European country ;) – Sverre Sep 13 '14 at 15:50
32

The footnote, which you haven't fully reproduced in the screenshot, provides the necessary explanation:

"Wir verwenden deutsche Buchstaben ..."

which may be translated as "we use German (i.e., Fraktur) letters..."

The two letters you've highlighted in yellow, by the way, are x and y (in Fraktur, of course).

Just as there are many (upright) Roman and Italic font faces, there are many Fraktur font faces. If you're interested in getting a reasonably faithful copy of the letters shown in the screenshot, you could do so by loading the yfonts package and using its command \textfrak to typeset the letters. (In the example below, I also make an attempt to mimic the "upright" shapes of the characters phi and psi.)

enter image description here

\documentclass{article}
\usepackage{yfonts,upgreek}  % 'upgreek' provides "upright" forms of \varphi and \psi
\begin{document}
$\upvarphi(\textfrak{x})=\uppsi(\textfrak{y})$
\end{document}

For what it's worth, I think that some of the letters produced by the \mathfrak macro of the eufrak package -- and the letter x in particular -- tend to look more "gothic" than "pure fraktur" to me.

  • 4
    Great job! :) (I'm out of votes, but I'll upvote this answer ASAP) I decided to check the English version of this paper (I happen to have an amusing book nearby me for some reason) and the footnotes match! :) In his previous paper, The completeness the axioms of the functional calculus of logic, Gödel uses and abuses Fraktur as his heart (or mind) desires. :) – Paulo Cereda Sep 13 '14 at 15:52
  • 1
    @Mico: Did you use the type 1 version of yfrak? – Bernard Sep 13 '14 at 16:18
  • @Bernard -- I think so. By the way, if I type \renewcommand{\frakdefault}{ysmfrak} before typesetting the equation, I get a much more jagged-looking result on screen -- the direct result of Metafont. This difference in looks makes me think that only the regular-size, but not the small variant of Yannis' fraktur font as well, was converted to Type 1 for the yfonts package. – Mico Sep 13 '14 at 16:27
9

It's fraktur x and y:

http://www.fileformat.info/info/unicode/char/1d535/fontsupport.htm
http://www.fileformat.info/info/unicode/char/1d536/fontsupport.htm

(....)

6

Symbols can be produced with:

\documentclass{article}
\usepackage{eufrak}
\begin{document}
$\mathfrak{x}$ and $\mathfrak{y}$
\end{document}

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