Implications

• Implications Home
• Code 1 Implications
• Code 2 Implications
• Code 3 Implications
• Code 4 Implications
• Code 5 Implications
• Code 6 Implications
• Complete List
• Search

We have the following indirect implication of form equivalence classes:

89 \(\Rightarrow\) 254 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
89 \(\Rightarrow\) 254	Variations of Zorn's lemma, principles of cofinality, and Hausdorff's maximal principle, Part I and II, Harper, J. 1976, Notre Dame J. Formal Logic

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number	Statement
89:	Antichain Principle:  Every partially ordered set has a maximal antichain. Jech [1973b], p 133.
254:	\(Z(D,R,l)\): Every directed relation \((P,R)\) in which ramified subsets have least upper bounds, has a maximal element.

Comment: