François G. Dorais

activity

20112017

most citedClassical consequences of continuous choice principles from intuitionistic analysis

19 citations · 28 across the 9 of their papers we have counts for

collaborators

10 papers

math.LO2017

When does every definable nonempty set have a definable element?

François G. Dorais, Joel David Hamkins

The assertion that every definable set has a definable element is equivalent over ZF to the principle $V = HOD$ , and indeed, we prove, so is the assertion merely that every $Π…

math.LO2016

Bounding 2D Functions by Products of 1D Functions

François Dorais, Dan Hathaway

Given sets $X, Y$ and a regular cardinal $μ$ , let $Φ (X, Y, μ)$ be the statement that for any function $f : X \times Y \to μ$ , there are functions $g_{1} : X \to μ$ and $g_{2} : Y \to μ$ s…

math.LO2014

Comparing the strength of diagonally non-recursive functions in the absence of $Σ_{2}^{0}$ induction

François G. Dorais, Jeffry L. Hirst, Paul Shafer

We prove that the statement "there is a $k$ such that for every $f$ there is a $k$ -bounded diagonally non-recursive function relative to $f$ " does not imply weak König's lemma over…

math.GT2013★ 2 cited

Isotopy and Homotopy Invariants of Classical and Virtual Pseudoknots

Francois Dorais, Allison Henrich, Slavik Jablan +1

Pseudodiagrams are knot or link diagrams where some of the crossing information is missing. Pseudoknots are equivalence classes of pseudodiagrams, where equivalence is generated by…

math.LO2012

Reverse Mathematics and Algebraic Field Extensions

François G. Dorais, Jeffry Hirst, Paul Shafer

This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section 2, we show that $WKL_{0}$ is equivalent to the ability…

math.LO2012★ 19 cited

Classical consequences of continuous choice principles from intuitionistic analysis