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math.LO2008
A Dedekind Finite Borel Set
Arnold W. Miller
In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if B is a G-delta-sigma set, then either…
math.LO2008
The Recursion Theorem and Infinite Sequences
Arnold W. Miller
In this paper we use the Recursion Theorem to show the existence of various infinite sequences and sets. Our main result is that there is an increasing sequence e_0, e_1, e_2 .. su…