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2 results

  • ELEMENTARY EQUIVALENCE IN POSITIVE LOGIC VIA PRIME PRODUCTS

  • Part of
  • TOMMASO MORASCHINI, JOHANN J. WANNENBURG, KENTARO YAMAMOTO
  • Journal:
    The Journal of Symbolic Logic , First View
    Published online by Cambridge University Press:
    05 July 2023, pp. 1-18
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  • We introduce prime products as a generalization of ultraproducts for positive logic. Prime products are shown to satisfy a version of Łoś’s Theorem restricted to positive formulas, as well as the following variant of the Keisler Isomorphism Theorem: under the generalized continuum hypothesis, two models have the same positive theory if and only if they have isomorphic prime powers of ultrapowers.

  • SPACES OF TYPES IN POSITIVE MODEL THEORY

  • LEVON HAYKAZYAN
  • Journal:
    The Journal of Symbolic Logic / Volume 84 / Issue 2 / June 2019
    Published online by Cambridge University Press:
    24 January 2019, pp. 833-848
    Print publication:
    June 2019

  • We introduce a notion of the space of types in positive model theory based on Stone duality for distributive lattices. We show that this space closely mirrors the Stone space of types in the full first-order model theory with negation (Tarskian model theory). We use this to generalise some classical results on countable models from the Tarskian setting to positive model theory.