Limiting Density and Free Structures

Abstract: Gromov had asked what a random group looks like - in a limiting density sense. I conjectured that the elementary frst order theory of the random group on n >= 2 generators, and with a single relator matches that of the non-Abelian free groups. Coulon, Ho, and Logan have proved that the theories match on universal sentences. We may ask Gromovs question for other varieties. Franklin and I looked for varieties for which calculating the limiting densities is easier. We have examples for which the elementary frst order theory of the random structure matches that of the free structure, and other examples for which the theories differ. (joint work with Johanna Franklin)

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

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