Pseudofinite and pseudocompact metric structures
Isaac Goldbring, Vinicius Cifu Lopes
TL;DR
This paper explores the concepts of pseudofiniteness and pseudocompactness in continuous logic, establishing their properties, relationships, and examples, and examines the behavior of definable functions in pseudofinite structures.
Contribution
It introduces the notion of pseudocompactness, investigates its relation to pseudofiniteness, and analyzes definable endofunctions in pseudofinite metric structures.
Findings
Pseudofiniteness and pseudocompactness have distinct basic properties.
Many examples illustrating these concepts are provided.
The injective-surjective behavior of definable functions in pseudofinite structures is studied.
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.
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