Zero-One Law Characterizations of ε0
Using methods and results from finite model theory and real analysis it is shown that the ordinal ε0 can be characterized as the first additive principal number for which certain zero-one laws for infinitary structures do not hold. As a contribution to problem 4.17 and problem 10.6 in Burris 2001  we show that additive principal numbers below εo yield additive number systems in RT1 and multiplicative number systems in RV0.
KeywordsNumber System Analytic Combinatorics Isomorphism Type Asymptotic Density Fundamental Identity
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