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

97
comparable classes (intspec). We have the following definition of
this idea:
intspec(z) = (', X"):, ' C:. z" C ': 3. Ne z' spec NVc'^":
cj a a a
With this definition we can build up the following definition
of the Axiom of Affinity (Affinax)
Affinax = (x, w): int spec (o). int spec (x). )
dl
Nc' spec Nc'. D. 3. Nc'Cls' spec Nc' (t" ):.
We see that Affinax cannot be applied to classes, which are
not self-comparable. Therefore we never can prove with thisaxiom
the multiplicative axiom or some equivalent axiom, It is easy to
see, although it can by no means be proved that Affinax is consistent with Transcax. If we take Transcax for Infinax and Affinax
for Multax, we get a system, which is as well founded as Cantor's
system, and which enables us to have a generalised Arithmetie
and Mathematical Analysis
Additional errata to Part I.
p. 20, 1.' 34, read epp for fq
p. 21, 1. 2, 3 and 4 read ~p for f
p. 23, 1. 16 read,,Fundamental class-letters" for,Fundamental and
functional class-letters".
p 24, 1. 26 read G(i2, ) for E(2,r)
p. 25, footnote read 0-14-141 for 0-13-131
*9'15 for X9'15
p. 25, footnote 3 read x for x, y for a
p. 26, 1. 22 read,,noted individual variables" for,,noted variables"
p. 26, 1. 24 read xy[q{xy/}]} Yx[p{xy}1 for x[(p{x}], px[(p{x}]
p. 28, 1. 8 read,,are to be used in E as denoting" for,,denote"
p. 28, 1. 17 read,expression or a real variable, E" for,expression, E"
p. 28, 1. 23 read,,we can make any substitution for a letter in
all its occurrences, allowed in the defining symbol" for,we
can take a functional expression for a determined real variable".