[The Hahn-Banach theorem by disjunction elimination]
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 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.
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DOI : 10.5802/cml.57
Mots-clés : Hahn-Banach theorem; Scott entailment relations; conservative extension; constructive mathematics.
Konstantin Schlagbauer 1 ; Peter Schuster 2 ; Daniel Wessel
CC-BY-NC-ND 4.0
@article{CML_2019__11_1_79_0,
author = {Konstantin Schlagbauer and Peter Schuster and Daniel Wessel},
title = {Der {Satz} von {Hahn-Banach} per {Disjunktionselimination}},
journal = {Confluentes Mathematici},
pages = {79--93},
publisher = {Institut Camille Jordan},
volume = {11},
number = {1},
year = {2019},
doi = {10.5802/cml.57},
mrnumber = {4002395},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.5802/cml.57/}
}
TY - JOUR AU - Konstantin Schlagbauer AU - Peter Schuster AU - Daniel Wessel TI - Der Satz von Hahn-Banach per Disjunktionselimination JO - Confluentes Mathematici PY - 2019 SP - 79 EP - 93 VL - 11 IS - 1 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.57/ DO - 10.5802/cml.57 LA - en ID - CML_2019__11_1_79_0 ER -
%0 Journal Article %A Konstantin Schlagbauer %A Peter Schuster %A Daniel Wessel %T Der Satz von Hahn-Banach per Disjunktionselimination %J Confluentes Mathematici %D 2019 %P 79-93 %V 11 %N 1 %I Institut Camille Jordan %U https://cml.centre-mersenne.org/articles/10.5802/cml.57/ %R 10.5802/cml.57 %G en %F CML_2019__11_1_79_0
Konstantin Schlagbauer; Peter Schuster; Daniel Wessel. Der Satz von Hahn-Banach per Disjunktionselimination. Confluentes Mathematici, Tome 11 (2019) no. 1, pp. 79-93. doi : 10.5802/cml.57. https://cml.centre-mersenne.org/articles/10.5802/cml.57/
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