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Nearly Model Complete Theories
Author(s) -
Kueker David W.,
Turnquist Brian P.
Publication year - 1999
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19990450302
Subject(s) - mathematics , model theory , diagram , point (geometry) , combinatorics , discrete mathematics , geometry , statistics
A theory T of a language L is 1‐model complete (nearly model complete) iff for every formula ρ of L there is a formula ϕ ( χ ) of L which is a ∀∃‐formula (a Boolean combination of universal formulas) such that T ⊨ ∀ x [ϕ↔θ]. The main results of the paper give characterizations of nearly model complete theories and of 1‐model complete theories. As a consequence we obtain that a theory T is nearly model complete iff whenever is a model of T and ⊆ 1 , then T ∪ Δ 1 is a complete L (A)‐theory, where Δ 1 is the 1‐diagram of . We also point out that our main results extend to ( n + l)‐model complete and nearly ra‐model complete theories for all n > 0.