Abstract
A theorem is effective iff it is proved in ZF°, where ZF° is ZermeloFraenkel set theory without the axioms of choice and foundation (regularity). A well known effective theorem of F. Riesz states that a Hubert space is finite dimensional iff its closed unit ball is compact. This may fail for sequential compactness. If U is a set of urelements, equipped with the structure of 12, / is the ideal of all finite subsets of U and G is the group of unitary operators, by an argument similar to [7]. In the resulting permutation model P(U,G,I), each orthonormal (= ON) system in U is finite. Therefore U is locally sequentially compact, but there is no ON base for U. A similar situation holds for the Dworetzky-Rogers characterisation of finite dimensional spaces ([9], Theorem I.e.2). But in combination we get the effective result:
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
