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Existentially Closed Models of Basic Number Theory

, 1977
This paper is concerned with a subtheory B of (first order) peano number theory P which is strong enough to contain many non-trivial number theoretic facts. We call this theory B basic number theory. Our aim is to give a complete description of the spectrum of (countable) models of B. Of course we will not achieve this aim here, but the results we give
H. Simmons
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Countable infinite existentially closed models of universally axiomatizable theories

Siberian Advances in Mathematics, 2016
Summary: We obtain a new criterion for a model of a universally axiomatizable theory to be existentially closed. The notion of a maximal existential type is used in the proof and for investigating properties of countable infinite existentially closed structures.
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Existentially closed exponential fields [PDF]

Israel Journal of Mathematics, 2021
We characterise the existentially closed models of the theory of exponential fields. They do not form an elementary class, but can be studied using positive logic. We find the amalgamation bases and characterise the types over them. We define a notion of
Jonathan Kirby, Kirby Jonathan
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Existential Morphisms and Existentially Closed Models of Logical Categories

Mathematical Logic Quarterly, 1981
Ioana Petrescu
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Existentially closed models via constructible sets: There are 2^ℵ0 existentially closed pairwise non elementarily equivalent existentially closed ordered groups

Journal of Symbolic Logic, 1996
AbstractWe prove that there are 2χ0 pairwise non elementarily equivalent existentially closed ordered groups, which solve the main open problem in this area (cf. [3, 10]).A simple direct proof is given of the weaker fact that the theory of ordered groups has no model companion; the case of the ordered division rings over a field k is also investigated ...
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Automorphisms of $$\kappa $$-existentially closed groups

Monatshefte Fur Mathematik, 2022
Burak Kaya, Mahmut Kuzucuoğlu
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Construction of existentially closed Abelian lattice-ordered groups using Fraïssé limits

Algebra Universalis, 2021
Brian Wynne
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Decidable fragments of universal theories and existentially closed models

Siberian Mathematical Journal, 1980
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Existentially Closed Closure Algebras

Notre Dame Journal of Formal Logic, 2020
Philip Scowcroft
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Countable existentially closed models for universally axiomatizable theories

Matematicheskie trudy, 2015
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