@article{10.5555_3173499.3173502,
    author = {Karzow, Alexander},
    title = {The field of the reals and the random graph are not finite-word ordinal-automatic},
    year = {2015},
    issue_date = {January 2015},
    publisher = {Otto-von-Guericke-Universitat},
    address = {DEU},
    volume = {20},
    number = {1},
    issn = {1430-189X},
    abstract = {Recently, Schlicht and Stephan lifted the notion of automatic-structures to the notion of (finite-word) ordinal-automatic structures. These are structures whose domain and relations can be represented by automata reading finite words whose shape is some fixed ordinal α. We lift Delhomm\'{e}'s relative-growth-technique from the automatic and tree-automatic setting to the ordinal-automatic setting. This result implies that the random graph is not ordinal-automatic and infinite integral domains are not ordinal-automatic with respect to ordinals below ω1 + ωω where ω1 denotes the first uncountable ordinal.},
    journal = {J. Autom. Lang. Comb.},
    month = {jan},
    pages = {27--43},
    numpages = {17},
    keywords = {Rado graph, automatic integral domains, growth rates, ordinal-automatic structures},
    date-added = {2025-11-16 7:37:40 +0100}
}

@article{10.5555_3173499.3173502, author = {Karzow, Alexander}, title = {The field of the reals and the random graph are not finite-word ordinal-automatic}, year = {2015}, issue_date = {January 2015}, publisher = {Otto-von-Guericke-Universitat}, address = {DEU}, volume = {20}, number = {1}, issn = {1430-189X}, abstract = {Recently, Schlicht and Stephan lifted the notion of automatic-structures to the notion of (finite-word) ordinal-automatic structures. These are structures whose domain and relations can be represented by automata reading finite words whose shape is some fixed ordinal α. We lift Delhomm\'{e}'s relative-growth-technique from the automatic and tree-automatic setting to the ordinal-automatic setting. This result implies that the random graph is not ordinal-automatic and infinite integral domains are not ordinal-automatic with respect to ordinals below ω1 + ωω where ω1 denotes the first uncountable ordinal.}, journal = {J. Autom. Lang. Comb.}, month = {jan}, pages = {27--43}, numpages = {17}, keywords = {Rado graph, automatic integral domains, growth rates, ordinal-automatic structures}, date-added = {2025-11-16 7:37:40 +0100} }