Pseudofinite and pseudocompact metric structures

Details Pseudofinite and pseudocompact metric structures Pseudofinite and pseudocompact metric structures

2011-09-10

arxiv.org/abs/1109.2246v2

Mathematics

Logic

Second version. Some typos fixed. Easier proofs in Section 5

Scientific paper

We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of pseudofiniteness and pseudocompactness and provide many examples. We also investigate the injective-surjective phenomenon for definable endofunctions in pseudofinite structures.

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