Submission date: 7 December 2018

Abstract:

Using the Feferman-Vaught Theorem, we prove that a definable subset of a product structure must be a Boolean combination of open sets, in the product topology induced by giving each factor structure the discrete topology. We prove a converse of the Feferman-Vaught theorem for families of structures with certain properties, including families of integral domains. We use these results to obtain characterizations of the definable subsets of ∏_p 𝔽_p -- in particular, every formula is equivalent to a Boolean combination of ∃∀∃ formulae.

Mathematics Subject Classification: 03C10 (Primary) 13L05 (Secondary)

Keywords and phrases:

Full text arXiv 1812.02905: pdf, ps.