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i0Computability Logic - http://en.wikipedia.org/wiki/Computability_logic - Wikipedia (free encyclopedia) article.
 
i0Infinitary Logic - http://plato.stanford.edu/entries/logic-infinitary/ - Article in the Stanford Encyclopaedia of Philosophy by John L. Bell. Infinitary Logic is a branch of formal logic where finitary formulae are replaced by potentially infinitary mathematical entities.
 
i0Logic System Interrelationships - http://www.cc.utah.edu/~nahaj/logic/structures/ - Shows how a number of representative logics fit together. The interrelationships usually given as something of the form: System X is system Y plus the axiom Z. By John Halleck.
 
i0Non Standard Logics - http://www.earlham.edu/~peters/courses/logsys/nonstbib.htm - A comprehensive listing of flavours of non-standard logic with brief descriptions and references, compiled by Peter Suber.
 
i0What are Weak Arithmetics - http://www.univ-paris12.fr/lacl/jaf/html/wa.html - Notes defining the subject. Available in HTML and PS formats.
 
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