Some Remarks on Weak Bisimilarity of BPA-Processes
Ivana Černá, Jitka Stříbrná · 2000
this paper we shall view ordinals as generalization of (the well-ordered nature of) natural numbers. Ordinal numbers form a class, denoted by On, and are well-ordered by the element-of relation <. The initial segment of On containing natural numbers and # is 0, 1, 2,...,n,...,#, after which follow # +1,#+2,...,#+ n,...,# + #, etc. The ordinals 0,#,#+ #,arelimit ordinals which means they have no predecessor, whereas ordinals such as 1, 2, and # +1,#+2,aresuccessor ordinals. We will be using the principle of ordinal or transfinite induction, the induction principle generalized to the class of all ordinal numbers. For a detailed instruction on ordinal numbers the reader should consult standard textbooks on set theory, such as [9].