Infinitary Noetherian constructions I. Infinite words

We define and study Noetherian topologies for spaces of infinite sets, and infinite words. In each case, we also obtain S-representations, namely, computable presentations of the sobrifications of those spaces.

[1]  Sylvain Schmitz,et al.  Demystifying Reachability in Vector Addition Systems , 2015, 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science.

[2]  C. St. J. A. Nash-Williams,et al.  On better-quasi-ordering transfinite sequences , 1968, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  Simon Halfon,et al.  On Effective Representations of Well Quasi-Orderings , 2018 .

[4]  Jean Goubault-Larrecq.  Non-Hausdorff Topology and Domain Theory - Selected Topics in Point-Set Topology , 2013, New Mathematical Monographs.

[5]  R. Rado.  Partial well-ordering of sets of vectors , 1954 .

[6]  Jean Goubault-Larrecq,et al.  On Noetherian Spaces , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).

[7]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[8]  Alberto Marcone,et al.  Foundations of BQO theory , 1994 .

[9]  Andrea Schalk,et al.  Algebras for generalized power constructions , 1993 .

[10]  Jean Goubault-Larrecq,et al.  Forward analysis for WSTS, part I: completions , 2009, Mathematical Structures in Computer Science.

[11]  Richard Laver,et al.  Mathematical Proceedings of the Cambridge Philosophical Society Well -quasi -orderings and sets of finite sequences , 2007 .

[12]  Graham Higman,et al.  Ordering by Divisibility in Abstract Algebras , 1952 .