The combinatorics of combinatorial coding by a real

Ramsey理想的组合性质

Combinatorics of Ramsey ideals

研究可数无限集上Ramsey型理想的组合性质，通过划分和收敛性质给出新刻画，并分析高维Ramsey定理的理想版本，引入Galvin理想作为中间概念。

Combinatorics of reductions between equivalence relations

We discuss combinatorial conditions for the existence of various types of reductions between equivalence relations, and in particular identify necessary and sufficient conditions for the existence of injective reductions.

A combinatorial forcing for coding the universe by a real when there are no sharps

Assuming 0# does not exist, we present a combinatorial approach to Jensen's method of coding by a real. The forcing uses combinatorial consequences of fine structure (including the Covering Lemma, in various guises), but makes no direct appeal to fine structure itself.

Some Combinatorics behind Proofs

We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that there is a generalization of the interpolation theorem to much more naive structures about sets, and then we show how both classical and intuitionistic versions of the statement follow by interpreting properly the set-theoretic language. The theorem we present is a geometrical formulation of the well-known logical statement and gives sufficient conditions for…

Hyperintegers and Nonstandard Techniques in Combinatorics of Numbers

In literature, many important combinatorial properties of subsets of N have been studied both with nonstandard techniques and from the point of view of N. In this thesis we mix these two different approaches in a technique that, at the same time, incorporates nonstandard tools and ultrafilters.

迭代星映射的基础及其在组合学中的应用

Foundations of iterated star maps and their use in combinatorics

本文为非标准分析中星映射的外部与内部迭代相互作用建立基础框架，并通过实例展示其在组合数论中的有效性与灵活性。