187 citations · 301 across the 16 of their papers we have counts for
9 papers · 1 filter
On the relationships between some meta-mathematical properties of arithmetical theories
Yong Cheng
In this work, we aim at understanding incompleteness in an abstract way via metamathematical properties of formal theories. We systematically examine the relationships between the…
There are no minimal effectively inseparable theories
Yong Cheng
This paper belongs to the research on the limit of the first incompleteness theorem. Effectively inseparable theories (EI) can be viewed as an effective version of essentially unde…
Effective inseparability and some applications in meta-mathematics
Yong Cheng
Effectively inseparable pairs and their properties play an important role in the meta-mathematics of arithmetic and incompleteness. Different notions are introduced and shown in th…
The Hypothesis and a supercompact cardinal
Yong Cheng
In this paper, we prove that: if is supercompact and the Hypothesis holds, then there is a proper class of regular cardinals in which are measurable in $\m…
The strong reflecting property and Harrington's Principle
Yong Cheng
In this paper we characterize the strong reflecting property for -cardinals for all , characterize Harrington's Principle and its generalization and discuss the rel…
Harrington's principle over higher order arithmetic
Yong Cheng, Ralf Schindler
Let , , and denote , , and order arithmetic, respectively. We let Harrington's Principle, {\sf HP}, denote the statement that t…
Indestructibility properties of remarkable cardinals
Yong Cheng, Victoria Gitman
Remarkable cardinals were introduced by Schindler, who showed that the existence of a remarkable cardinal is equiconsistent with the assertion that the theory of is…
Large cardinals need not be large in HOD
Yong Cheng, Sy-David Friedman, Joel David Hamkins
We prove that large cardinals need not generally exhibit their large cardinal nature in HOD. For example, a supercompact cardinal need not be weakly compact in HOD, and there c…
Force a set model of + Harrington's Principle
Yong Cheng
Let denote order arithmetic. Let Harrington's Principle, HP, denote the statement that there is a real such that every --admissible ordinal is a cardinal in $…