Unary functions

作者：Sokic Miodrag^*

来源：European Journal of Combinatorics, 2016, 52: 79-94.

DOI：10.1016/j.ejc.2015.09.003

We consider F the class of finite unary functions, 2 the class of finite bijections and F-k, k > 1, the class of finite k - 1 functions. We calculate Ramsey degrees for structures in F and F-k, and we show that 2 is a Ramsey class. We prove Ramsey property for the class OF which contains structures of the form (A, f, <=) where (A, f) is an element of F and <= is a linear ordering on the setA. We also consider a generalization MnF, n > 1, of the class F which contains finite structures of the form (A,, where eachf(i) is a unary function on the set A. Finally we give a topological interpretation of our results by expanding the list of extremely amenable groups and by calculating various universal minimal flows.

• 出版日期2016-2