The theory of constructive types (principles of logic and mathematics). By Leon Chwistek.

23
0o061 If >, is an individual (0o primitive, or fundamental) letter, X is
an individual (orpr primitive, or fundamental) a p p a r e n t v a
riab le.
0'062 An expression on ntaining only onee individual (or primitive,
or fundamental) letter. k and no other letters and symbols,
is an individual (o)r primitive, or fundamental) real variable.
0'0"7 Expressions z?, y S are fun tio nal c 1 ass-le tters.,
0'071 Expression s L,.M, T are f, u n e t i o n a r l a t io - t et c r s.
0'072 Functional class-letters are fu n eti o n al expressions with
I variable.
007 3 Funetion al relation-detters are f unc t ion a e x p r e s s i o n s
with II variables.
0'08 Espressions, iT x are funda r en-tal elass-lette rs
0'081 Expressions Pi Q,.1f S are f'u n d a m e n t a1 relations -letterso
0-082 Expressions a v, wc t are de teri in i ed letters.
0'083 Fundamental and funetionel class-let;ters, fundamental relation
letters and determined letters are f u n d a m e n t a 1 e t t e r s.
0'09 Expressions c, b, e d are p s e u d o-l e tter s
0'091 Al pseudo-letters occurring in a given expression stand for
functional elass-letters or relation-letters.
0'092 If X is a fundaimen:tal elass- (or relation-) letter, (or a:tuntioî
nal class- or relation-letter, or a determined, or a pseudo.
letter), theii 7,' is a fundamental elass- (or relation.) letter,
(or a functional class-or relation-lletter, or a determiinted, or a
pseudo-letter).
0'10. E x p r e s s i o s.
0(11 If ]i' F are expressions denoting logical propositions, then. il F7 denotes logical proposition 1)
Remark: The dots are can essential part of the expression.E;F
Note that there is n1o need of a father theory of dots. For
this theory of dots I am indebted to Prof. Les niewski. The
idea of p q was introduced by Mr. Shefler 2). If we use the
1) Numbers 0 1-11 correspond to t;; 1'771 of Principia. Logical propositions
make up the lowest type of propositions. i n our ystomr there are no other propositions. Nevertheless, if It i. speaking' aboit ioicall propositions,, I II ii working
with propositions which aie not logical.
2) Transations of Anericnn IMathemnatical, society 19 i 3.