English

Pseudofinite and pseudocompact metric structures

Logic 2016-02-10 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1109.2246,
  title  = {Pseudofinite and pseudocompact metric structures},
  author = {Isaac Goldbring and Vinicius Cifu Lopes},
  journal= {arXiv preprint arXiv:1109.2246},
  year   = {2016}
}

Comments

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

R2 v1 2026-06-21T19:03:01.828Z