# A flaw in separation axioms ?

There are only enumerably many properties that can be constructed from **formula** strings, as these are finite strings of characters from a finite alphabet. Axiomatic set theory is **basis-incomplete** in the sense that e.g. the **continuum hypothesis** can neither be proven nor its negation. A closer look at **formula** strings leads to a very deep **problem** that the author has not found to be discussed in the literature:

There exist unary **formula** strings that are **neither true nor false** for some instances. Can the * Axioms of Separation *(that are based on formula strings) be repaired to circumnavigate the fact that they can lead to sentences that are not true? The author does not see a way out. Do you ?

Download PDF-file 'A Flaw in Separation Axioms', version 1.2 (20 pages) , first publication version 1.0 for priority 25.09.2019 viXra: 1909.0531

*For the reader who does not want to go into the details of the FUME-method the problem is sketched in a letter using conventional notation on the next page.*