arXiv subjects

Katie Brodhead

Publications and source records attributed to Katie Brodhead.

2 recordsLinked to original sources

arXiv2019

The Strength of the Grätzer-Schmidt Theorem

The Grätzer-Schmidt theorem of lattice theory states that each algebraic lattice is isomorphic to the congruence lattice of an algebra. We study the reverse mathematics of this theorem. We also show that the set of indices of computable lattices that are complete is $Π^1_1$-complete; the set of indices of computable lattices that are algebraic is $Π^1_1$-complete; the set of compact elements of a computable lattice is $Π^{1}_{1}$ and can be $Π^1_1$-complete; and the set of compact elements of a distributive computable lattice is $Π^{0}_{3}$, and there is an algebraic distributive computable lattice such that the set of its compact elements is $Π^0_3$-complete.

math.LO↗

arXiv2014

Numberings and randomness

We prove various results on effective numberings and Friedberg numberings of families related to algorithmic randomness. The family of all Martin-Löf random left-computably enumerable reals has a Friedberg numbering, as does the family of all $Π^0_1$ classes of positive measure. On the other hand, the $Π^0_1$ classes contained in the Martin-Löf random reals do not even have an effective numbering, nor do the left-c.e. reals satisfying a fixed randomness constant. For $Π^0_1$ classes contained in the class of reals satisfying a fixed randomness constant, we prove that at least an effective numbering exists.

math.LO↗