Der Satz von Hahn-Banach per Disjunktionselimination
Confluentes Mathematici, Volume 11 (2019) no. 1, p. 79-93

Der Erweiterungssatz von Hahn-Banach ist zugleich ein Stützpfeiler der Funktionalanalysis und — infolge seiner bekannten Natur als Konsequenz des Auswahlaxioms — Musterbeispiel für eine reine Existenzaussage. Vermöge eines allgemeinen syntaktischen Konservativitätsresults bezüglich mehr- über einwertigen Schlussrelationen können wir den Satz von Hahn-Banach auf eine Disjunktionselimination zurückführen. Semantische Interpretation erlaubt sodann Rückschluss auf das klassische Resultat.

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.

Received : 2018-07-17
Revised : 2018-11-28
Accepted : 2018-07-12
Published online : 2019-08-28
DOI : https://doi.org/10.5802/cml.57
Classification:  03F65,  06F20
Keywords: Hahn-Banach theorem; Scott entailment relations; conservative extension; constructive mathematics.
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     author = {Konstantin Schlagbauer and Peter Schuster and Daniel Wessel},
     title = {Der Satz von Hahn-Banach per Disjunktionselimination},
     journal = {Confluentes Mathematici},
     publisher = {Institut Camille Jordan},
     volume = {11},
     number = {1},
     year = {2019},
     pages = {79-93},
     doi = {10.5802/cml.57},
     language = {en},
     url = {https://cml.centre-mersenne.org/item/CML_2019__11_1_79_0}
}
Schlagbauer, Konstantin; Schuster, Peter; Wessel, Daniel. Der Satz von Hahn-Banach per Disjunktionselimination. Confluentes Mathematici, Volume 11 (2019) no. 1, pp. 79-93. doi : 10.5802/cml.57. https://cml.centre-mersenne.org/item/CML_2019__11_1_79_0/

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