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We examine the reverse-mathematical strength of several theorems in classical and effective model theory concerning first-order theories and their number of models. We prove that, among these, most are equivalent to one of the familiar systems RCA0, WKL0, or ACA0. We are led to a purely model-theoretic statement that implies WKL0 but refutes ACA0 over RCA0.



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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
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