With Raoult’s Open Induction in place of Zorn’s Lemma, we do a perhapsmore perspicuous proof of Lindenbaum’s Lemma for not necessarily countable lan-guages of first-order predicate logic. We generally work for and with classical logic,but say what can be achieved for intuitionistic logic, which prompts the naturalgeneralizations for distributive and complete lattices.
Lindenbaum’s Lemma via Open Induction
Schuster, Peter Michael
2016-01-01
Abstract
With Raoult’s Open Induction in place of Zorn’s Lemma, we do a perhapsmore perspicuous proof of Lindenbaum’s Lemma for not necessarily countable lan-guages of first-order predicate logic. We generally work for and with classical logic,but say what can be achieved for intuitionistic logic, which prompts the naturalgeneralizations for distributive and complete lattices.
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