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 unresolved
Keywords isomorphism relation   Scott rank   mono-unary algebras
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DOI 10.1305/ndjfl/1172787543
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References found in this work BETA

An Example Concerning Scott Heights.M. Makkai - 1981 - Journal of Symbolic Logic 46 (2):301-318.
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.
Some Dichotomy Theorems for Isomorphism Relations of Countable Models.Su Gao - 2001 - Journal of Symbolic Logic 66 (2):902-922.

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