Leo Liberti's pages --- Other mathematical interests

History of Mathematics

Logic and Set Theory

  • A short account of my doubts about Goedel's theorem.
  • Very old projects from my days at Turin University:
    • ZFC is not finitely axiomatizable (in Italian only, sorry!).
    • Category Theory as an axiom system equivalent to ZFC (in Italian only, sorry!). This paper contains a subtle mistake. The mistake was found back in 1997 by Alessandro Andretta, professor of logic and set theory at Turin University, and for the life of me I can't remember exactly what it was. I seem to vaguely recall that there was some kind of trouble in formalizing a countably infinite number of axioms of ZFC with a finite number of axioms of Category Theory. I'm sure it was something along these lines.
    • For each field F there is a Galois extension E such that each ideal of the ring of integers of F is principal in the ring of integers of E (in Italian only, sorry!).


  • Here is an introduction to cryptography for the mathematically challenged (PDF).
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