The Hahn-Banach extension theorem is at once main pillar of functional analysis and — due to its notorious nature as consequence of the axiom of choice — prime example of a pure existential statement. By way of a general syntactic conservation result for multi-conclusion entailment relations on top of their single-conclusion counterparts, we are able to trace back the Hahn-Banach theorem to a disjunction elimination. The classical result can then be regained by semantic interpretation.

Der Satz von Hahn-Banach per Disjunktionselimination

Peter Schuster
;
Daniel Wessel
2019-01-01

Abstract

The Hahn-Banach extension theorem is at once main pillar of functional analysis and — due to its notorious nature as consequence of the axiom of choice — prime example of a pure existential statement. By way of a general syntactic conservation result for multi-conclusion entailment relations on top of their single-conclusion counterparts, we are able to trace back the Hahn-Banach theorem to a disjunction elimination. The classical result can then be regained by semantic interpretation.
conservative extension
constructive mathematics
Scott entailment relations
Hahn-Banach theorem
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1000081
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