13 citations · 22 across the 7 of their papers we have counts for
8 papers
The Limits of Arithmetical Pluralism: Incompleteness, Large Cardinals, and Graded Non-Pluralism
Yong Cheng
Gödelian incompleteness yields arithmetical sentences \(A\) such that \(\mathsf{PA}+A\) and \(\mathsf{PA}+\neg A\) are both consistent. Are such extensions equally legitimate? I pr…
On the depth of Wiles's proof of Fermat's Last Theorem
Yong Cheng, Colin McLarty
What constitutes depth in a mathematical proof? This paper addresses this foundational question through a close case study of Andrew Wiles's proof of Fermat's Last Theorem. We prop…
On Rosser theories
Yong Cheng
Rosser theories play an important role in the study of the incompleteness phenomenon and meta-mathematics of arithmetic. In this paper, we first define the notions of -Rosser th…
The limitless First Incompleteness Theorem
Yong Cheng
This work is motivated by the problem of finding the limit of the applicability of the first incompleteness theorem (). A natural question is: can we find a minimal theory…
Current research on Gödel's incompleteness theorems
Yong Cheng
We give a survey of current research on Gödel's incompleteness theorems from the following three aspects: classifications of different proofs of Gödel's incompleteness theorems, th…
On the depth of Gödel's incompleteness theorem
Yong Cheng
In this paper, we use Gödel's incompleteness theorem as a case study for investigating mathematical depth. We take for granted the widespread judgment by mathematical logicians tha…
Finding the limit of incompleteness I
Yong Cheng
In this paper, we examine the limit of applicability of Gödel's first incompleteness theorem ( for short). We first define the notion " holds for the theory ". T…
Gödel's incompleteness theorem and the Anti-Mechanist Argument: revisited
Yong Cheng
This is a paper for a special issue of the journal "Studia Semiotyczne" devoted to Stanislaw Krajewski's paper [30]. This paper gives some supplementary notes to Krajewski's [30] o…