Sentence:  Equivalently, it says that all relations of <WSD>adicity</WSD> greater than 3 may be reduced to relations of <WSD>adicities</WSD> 1, 2, and/or 3. The negative component of the Thesis says, first, that relations of <WSD>adicity</WSD> 2 may not "in general" be constructed from (reduced to) relations exclusively of <WSD>adicity</WSD> 1; and, second, that relations of <WSD>adicity</WSD> 3 and greater may not "in general" be constructed from (equivalently: reduced to) relations exclusively of <WSD>adicities</WSD> 1 and/or 2. 
Meaning of the word marked with <WSD> tags:  The number of arguments or operands a function or operation takes. For a relation, the number of domains in the corresponding Cartesian product.