Correspondence:
[*]
Address for correspondence: Institute of Philosophy, University of Warsaw Krakowskie Przedmieście 3, 00-927 Warsaw, Poland
Note: [†] The author was supported by the Polish National Science Centre grant 2013/11/B/HS1/04168.
Abstract: Modulus of a computable approximation is a function which returns the number of a stage at which the approximation has already converged for its argument. The least modulus points at the earliest such stage for each of its arguments. We recall and show some properties of least moduli, including their close connection to c.e. degrees, and minimal witnessing functions for FM-representable sets. We observe, for instance, that the non-density theorem for the d.c.e. degrees gives an example of an incomplete degree that has no least moduli below 0_′. Using the properties of least moduli themselves, we construct a degree containing no least moduli for itself and having least moduli of incomparable degrees. In particular, the technique used demonstrates an approach of constructing a non-c.e. degree, which is somewhat different from that proposed by Cooper.
