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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 ?


ASTsaf1.2.pdf (658.47KB)
ASTsaf1.2.pdf (658.47KB)

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.