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Abstract: it cannot express a variety of properties. For example, it follows immediately that evenness is not expressible in FO. Indeed, n (even) is 1 if n is even and 0 if n is odd. Thus, n (even) does not converge, so evenness is not expressible in any language that has a 0-1 law. While 0-1 laws provide an elegant and powerful tool, they require the development of some non-trivial machinery. Interestingly, this is one of the rare occasions when it is needed to consider infinite structures while... (Update)
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BibTeX entry: (Update)
@misc{ here-laws,
author = "We Present Here",
title = "0-1 Laws for FO",
url = "citeseer.ist.psu.edu/359263.html" }
Citations (may not include all citations):81 Probabilities on finite models (context) - Fagin - 1976
49 Range and degree of realizability of formulas in the restric.. (context) - Glebski, Kogan et al. - 1969
35 Information and Computation (context) - Kolaitis, Vardi et al. - 1992
20 A zero-one law for logic with a fixed point operator (context) - Blass, Gurevich et al. - 1985
16 Universal Graphs and Universal Functions (context) - Rado - 1964
3 The asymptotic truth value of infinite formulas (context) - Talanov, Knyazev - 1984
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