Abstract
Topological model theory is getting “en vogue”. It stems from the fact that model theory has been very successful1 for algebraic structures, clarifying algebraic concepts (algebraic closure, Lefshetz principles etc) and the concept of infinitesimals (non-standard analysis) and recently is even invading “hard” algebra (Whitehead's conjecture). It was always considered unsatisfactory that topological spaces could not be treated within the model theory of first order languages. It was usually argued that topology is basically a second order concept and even in ROBINSON'S book “Non-standard analysis” [ 301 non-standard topologies are non-standard models of the full structure over the topological space.
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Makowsky, J.A. (2010). Topological Model Theory. In: Mangani, P. (eds) Model Theory and Applications. C.I.M.E. Summer Schools, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11121-1_4
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