57 citations · 78 across the 5 of their papers we have counts for
7 papers
When Bi-interpretability implies Synonymy
Harvey M. Friedman, Albert Visser
Two salient notions of sameness of theories are synonymy, also known as definitional equivalence, and bi-interpretability. Of these two definitional equivalence is the strictest no…
Integration on the Surreals: a Conjecture of Conway, Kruskal and Norton
Ovidiu Costin, Philip Ehrlich, Harvey M. Friedman
In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field No of surreal numbers containing the reals and the ordinals, as well as a vast array of less fami…
Foundational aspects of singular integrals
Ovidiu Costin, Harvey M. Friedman
We investigate integration of classes of real-valued continuous functions on (0,1]. Of course difficulties arise if there is a non- element in the class, and the Hadamard fini…
Expansions of the real field by open sets: definability versus interpretability
H. Friedman, K. Kurdyka, C. Miller +1
An open set U of the real numbers R is produced such that the expansion (R,+,x,U) of the real field by U defines a Borel isomorph of (R,+,x,N) but does not define N. It follows tha…
A language for mathematical knowledge management
Steven Kieffer, Jeremy Avigad, Harvey Friedman
We argue that the language of Zermelo Fraenkel set theory with definitions and partial functions provides the most promising bedrock semantics for communicating and sharing mathema…
Combining decision procedures for the reals
Jeremy Avigad, Harvey Friedman
<p>We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider met…
Finite functions and the necessary use of large cardinals
Harvey M. Friedman
We present a coherent collection of finite mathematical theorems some of which can only be proved by going well beyond the usual axioms for mathematics. The proofs of these theorem…