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Complexity Ranks of Countable Models
Notre Dame Journal of Formal Logic 48 (1):33-48 (2007)
Abstract
We define some variations of the Scott rank for countable models and obtain some inequalities involving the ranks. For mono-unary algebras we prove that the game rank of any subtree does not exceed the game rank of the whole model. However, similar questions about linear orders remain unresolvedOther Versions
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Citations of this work
An introduction to the Scott complexity of countable structures and a survey of recent results.Matthew Harrison-Trainor - 2022 - Bulletin of Symbolic Logic 28 (1):71-103.
References found in this work
A complete L ω1ω-sentence characterizing ℵ1.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):59-62.
Some dichotomy theorems for isomorphism relations of countable models.Su Gao - 2001 - Journal of Symbolic Logic 66 (2):902-922.
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