Mathematical Logic Quarterly 46 (4):435-452 (2000)

We prove a 0-1 law for the fragment of second order logic SO over parametric classes of finite structures which allow only one unary atomic type. This completes the investigation of 0-1 laws for fragments of second order logic defined in terms of first order quantifier prefixes over, e.g., simple graphs and tournaments. We also prove a low oscillation law, and establish the 0-1 law for Σ14 without any restriction on the number of unary types
Keywords 0‐1 laws  Second order logic  Finite model theory
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DOI 10.1002/1521-3870(200010)46:4
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