The sets of real and complex numbers are denumerable

While most polynomial Julia sets are computable, it has been recently shown [12] that there exist non-computable Julia sets. The proof was non-constructive, and indeed there were doubts as to whether specific examples of parameters with non-computable ...

The notion of immune sets is extended to closed sets and $\Pi^0_1$ classes in particular. We construct a $\Pi^0_1$ class with no computable member which is not immune. We show that for any computably inseparable sets <em>A</em> and <em>B</em> , the ...

Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition, defined as S+T={m+n∣m∈S,n∈T}, and with ultimately ...