Assuming the existence of a measurable cardinal, we define a hierarchy of Ramsey cardinals and a hierarchy of normal filters. We study some combinatorial properties of this hierarchy. We show that this hierarchy is absolute with respect to the Dodd-Jensen core model, extending a result of Mitchell which says that being Ramsey is absolute with respect to the core model.

We prove that Rado's Conjecture implies that the nonstationary ideal on ω 1 is presaturated.

This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters are by leading experts in mathematical and philosophical logic that examine various aspects of the foundations of mathematics. The theme of the volume focuses on two basic foundational questions: (i) What is the nature of mathematical truth and how does one resolve questions that are formally unsolvable (...) within the Zermelo Fraenkel Set Theory with the Axiom of Choice, and (ii) Do the discoveries in mathematics provide evidence favoring one philosophical view over others? These issues are discussed from the vantage point of recent progresses in foundational studies. The final chapter features questions proposed by the participants of the Workshop that will drive foundational research. The wide range of topics covered here will be of benefit to students, researchers and mathematicians interested in the foundations of mathematics. (shrink)

This study explored the syntactic transfer effect of the non-local subject-verb agreement structure with plural head noun after two intensive phases of input training with event-related potentials (ERP). The non-local subject-verb agreement stimuli with the plural head nouns, which never appeared in training phases, were used for the stimuli. A total of 26 late L1-Chinese L2-English learners, who began to learn English after a critical period and participated in our previous experiments, were asked back to take part in this syntactic (...) transfer experiment. Results indicated that a significant ERP component P600 occurred in the key region (the verb) of the sentences with syntactic violations in the experimental group, but none occurred in the control group. This demonstrated that there was a significant transfer effect of the input training. The possible theoretical explanation was provided and also the malleability of the late L2 learners was discussed. (shrink)

This book is an abridged version of Feng Qi’s two major works on the history of philosophy, The Logical Development of Ancient Chinese Philosophy and The Revolutionary Course of Modern Chinese Philosophy. It is a comprehensive history of Chinese philosophy taking the reader from ancient times to the year 1949. It illuminates the characteristics of traditional Chinese philosophy from the broader vantage point of epistemology. The book revolves around important debates including those on “Heaven and humankind” (tian ren天人), “names and (...) actualities” (mingshi名實), “principle and vital force” (liqi理氣), “the Way and visible things” (daoqi道器), “mind and matter/things” (xinwu心物), and “knowledge and action” (zhixing知行). Through discussion of these debates, the course of Chinese philosophy unfolds. Modern Chinese philosophy has made landmark achievements in the development of historical and epistemological theory, namely the “dynamic and revolutionary theory of reflection”. However, modern Chinese philosophy is yet to construct a systematic overview of logic and methodology, as well as questions of human freedom and ideals. Amid this discussion, the question of how contemporary China is to “take the baton” from the thinkers of the modern philosophical revolution is addressed. (shrink)

We show that a cardinal κ is a (strongly) Mahlo cardinal if and only if there exists a nontrivial κ-complete κ-normal ideal on κ. Also we show that if κ is Mahlo and λ ≥ κ and $\lambda^{ then there is a nontrivial κ-complete κ-normal fine ideal on P κ (λ). If κ is the successor of a cardinal, we consider weak κ-normality and prove that if κ = μ + and μ is a regular cardinal then (1) $\mu^{ if (...) and only if there is a nontrivial κ-complete weakly κ-normal ideal on κ, and (2) if $\mu^{ then there is a nontrivial κ-complete weakly κ-normal fine ideal on P κ (λ). (shrink)

We give a new characterization of λ-supercompact cardinal κ in terms of -Solovay pairs. We give some applications of -Solovay pairs.

We show that $M \models \kappa$ is a completely Ramsey cardinal iff there is a Rowbottom M-ultrafilter on κ.

本书分上、下两册,上册自先秦至唐代,下册自宋代至清末民初。本书主要收入各时代的主要学派、主要哲学的代表性作品。.

With the increasing proportion of the logistics industry in the economy, the study of the vehicle routing problem has practical significance for economic development. Based on the vehicle routing problem, the customer presence probability data are introduced as an uncertain random parameter, and the VRP model of uncertain customers is established. By optimizing the robust uncertainty model, combined with a data-driven kernel density estimation method, the distribution feature set of historical data samples can then be fitted, and finally, a distributed (...) robust vehicle routing model for uncertain customers is established. The Q-learning algorithm in reinforcement learning is introduced into the high-level selection strategy using the hyper-heuristic algorithm, and a hyper-heuristic algorithm based on the Q-learning algorithm is designed to solve the problem. Compared with the certain method, the distributed robust model can effectively reduce the total cost and the robust conservatism while ensuring customer satisfaction. The improved algorithm also has good performance. (shrink)