With Raoult’s Open Induction in place of Zorn’s Lemma, we do a perhaps more perspicuous proof of Lindenbaum’s Lemma for not necessarily countable languages 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 natural generalizations for distributive and complete lattices.
Lindenbaum’s Lemma via Open Induction
CIRAULO, FRANCESCO;
2016
Abstract
With Raoult’s Open Induction in place of Zorn’s Lemma, we do a perhaps more perspicuous proof of Lindenbaum’s Lemma for not necessarily countable languages 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 natural generalizations for distributive and complete lattices.
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