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We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy . Each contains all spreading models generated by ℱ-sequences with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.
S. A. Argyros, V. Kanellopoulos, and K. Tyros. "Higher order spreading models." Fundamenta Mathematicae 221.1 (2013): 23-68. <http://eudml.org/doc/286676>.
@article{S2013, abstract = {We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences $(x_\{s\})_\{s∈ℱ\}$ with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy $(ℳ_\{ξ\}(X))_\{ξ<ω₁\}$. Each $ℳ_\{ξ\}(X)$ contains all spreading models generated by ℱ-sequences $(x_\{s\})_\{s∈ℱ\}$ with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.}, author = {S. A. Argyros, V. Kanellopoulos, K. Tyros}, journal = {Fundamenta Mathematicae}, keywords = {spreading models; Ramsey theory; thin families; plegma families; order of a family}, language = {eng}, number = {1}, pages = {23-68}, title = {Higher order spreading models}, url = {http://eudml.org/doc/286676}, volume = {221}, year = {2013}, }
TY - JOUR AU - S. A. Argyros AU - V. Kanellopoulos AU - K. Tyros TI - Higher order spreading models JO - Fundamenta Mathematicae PY - 2013 VL - 221 IS - 1 SP - 23 EP - 68 AB - We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences $(x_{s})_{s∈ℱ}$ with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy $(ℳ_{ξ}(X))_{ξ<ω₁}$. Each $ℳ_{ξ}(X)$ contains all spreading models generated by ℱ-sequences $(x_{s})_{s∈ℱ}$ with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy. LA - eng KW - spreading models; Ramsey theory; thin families; plegma families; order of a family UR - http://eudml.org/doc/286676 ER -